eratosthenes experiment

Science in School

The eratosthenes experiment: calculating the earth’s circumference teach article.

Author(s): Sevasti Malamou, Vasileios Kitsakis

On the shoulders of giants: follow in the footsteps of Eratosthenes and measure the circumference of the Earth like he did 2300 years ago.

The following learning scenario is made for secondary school students that are familiar with the concepts of equal angles, from geometry, and tangents, from trigonometry. Moreover, it can also be adjusted for primary school students not familiar with trigonometry: they can make measurements like Eratosthenes did and leave advanced calculations for the teacher.

Brief description

Students can measure the Earth’s circumference like Eratosthenes did approximately 2300 years ago using simple materials and a stick’s shadow made by the Sun. Even though there is a high probability that the measurement will not approximate the true value of the Earth’s circumference, like we know it today, the measuring itself provides a basis for simple mathematical reasoning and scientific thinking.  

Ideally, the experiment should take place on the March or September equinoxes on a sunny, or almost sunny, day. Before starting to measure the Earth’s circumference, students should learn about Eratosthenes, his life, work, and the way he calculated the circumference of the Earth.

Learning objectives

• Describe the geometry of sunlight towards Earth (sunrays are parallel when falling to Earth)
• Understand that equinoxes and solstices are due to the Earth’s movement
• Realize the geographic coordinate system of Earth: latitude and longitude
• Describe how Eratosthenes measured the circumference of the Earth
• Measure angles and distances
• Compare angles and triangles
• Explain measurement errors and suggest ways to minimize them
• Collaborate with other schools on the same longitude

Optional introductory activity: Who was Eratosthenes? Why is his experiment so important nowadays?

Although it seems a simple and easy experiment, it takes time for students to really understand geometry, the direction of the Sun towards Earth on specific days, and the logical sequence of Eratosthenes’ thoughts. 

The goal is not simply to measure the length of the stick and its shadow, but to understand Eratosthenes’ logic behind these simple measurements, and thus, highlight his ingenuity, since almost 2300 years ago he calculated the circumference of the Earth with relatively great accuracy.

We recommend carrying out the introductory activity , so that students understand the importance of Eratosthenes’ experiment, the era during which he did his experiment, what helped him to reach to his conclusions, and the way he managed to accomplish his experiment.

Activity 1: Identify the exact time of the measurement

Before implementing the experiment, which is actually to measure distances and make calculations, we must first determine when the Sun reaches its highest point in the sky on the day of the equinox; what we call local noon (or zenith). This time differs for each school and depends on the school’s position on the globe and should be determined with the best accuracy possible. At this specific time, sunrays fall perpendicularly on the equator, and they are parallel to the equatorial plane, so a vertical bar will have no shadow. On the other hand, in our place at this specific time, a vertical bar will have a shadow.

A calculator tool that can be used is SunCalc . The position and date have to be filled in for the Sun’s culmination time to be calculated. At this exact time on the day of the equinox, students have to measure the stick’s length and its shadow.

This activity only takes a few minutes, but it is also recommended to do the introductory activity to set the context. It should be possible to do the introductory activity and Activities 1 and 2 in one lesson; these should be completed a few days before the measurement lesson on the equinox (Activity 3).

• Internet connection and a suitable device (PC, laptop, tablet, smartphone)

At least 1–2 days before the equinox (when the measurements will be made), you should:

• Explain the experiment (ideally using the introductory activity ).
• Tell your students that many schools are doing this experiment on this specific day.
• Split your class into groups of two students and let them run the web tool SunCalc in the computer lab or use tablets.

• Find their city/village and school on the map
• Select the required date that the measurements are going to be made (equinoxes are preferred)
• Write down the culmination time

Alternatively, if you don’t have enough time or equipment, you can demonstrate the procedure.

Finding the zenith time for the Sun should only take a few minutes. You can also use the application as a learning object for students and ask them to investigate different sundial characteristics. The tool gives the chance to understand the concept of noon during the year. Students can change the date, and then see the culmination time for each date. Solstices and equinoxes are dates that should be investigated. Local noon is in the midpoint between sunrise and sunset times, and it depends on the latitude and date during the year.

Activity 2: Identify the school’s coordinates

At least one day before the experiment, students should identify the school’s coordinates using online tools. What is to be measured is the distance in kilometres from the schoolyard to the equator along the school’s meridian, which is going to be a curved line, following the Earth’s curvature. All points along this meridian have the same longitude.

Eratosthenes knew the distance between Alexandria and Syene (nowadays Aswan) in stadia (an ancient unit of length). Nowadays, we can measure the distance using electronic applications. You could also get a distance estimate using a real map and a ruler, just like students used to calculate real distances years ago. Especially for younger students, it would be a great chance to refresh their knowledge of map scales. The measurement won’t be as accurate as the one with online tools, but it is a simple estimation.

This activity should only take 10 min.

• Video on how to measure the distance from your school to the equator
• Alternatively, a map and a ruler
• Use a smartphone with a location function.
• Write down the latitude and longitude of the schoolyard.
• Measure the distance from your school to the equator. For this step, Google Maps or Google Earth can be used, as shown in the video .
• Write down the distance in kilometres. This information is what students need for their calculations.

Activity 3: Measure like Eratosthenes on the equinox

The day that everyone was expecting has arrived. The teacher has to organize all the required materials before the time that the Sun reaches its highest point. Everything should be prepared in advance because, once the Sun reaches its zenith, there is no time to lose. Students have to act quickly, and they have to know exactly what to do.

• Linear sticks (approximately 1 m long is ideal)
• Right-angle triangles, plumb bobs, carpenter’s levels, or an object that has a right angle to ensure verticality
• Metre sticks or tape measures
• Clock accurate to the minute (or a smartphone)

Student worksheet

• To measure the length of the sticks when the Sun is overhead, supply students with the necessary materials and worksheet a short time before the measurement time.
• Go with your students into the schoolyard at least 10–15 min before the zenith time for your latitude.
• Split the class into groups of four.
• Ask each member of the group to take on a specific role. Student 1 will be responsible for the time, student 2 will act as a scribe and record the measurements, and students 3 and 4 will do the measurements.
• Make sure that each group has a set of materials (a linear stick, a metre stick, a right-angle triangle, a pencil, a clock, and a worksheet).
• Ask students to measure the length of the stick before the zenith time and write their measurements on the worksheet.
• About 2–3 min before the zenith time, ask students to place and hold the sticks vertically.
• Use the right-angle triangle to make sure that the sticks are vertical. Check that all groups achieve verticality.
• When the Sun reaches its highest point in the sky, ask students to measure the stick’s shadow on the ground and write its value on the worksheet.
• If students don’t manage to measure the stick’s length before the zenith time, or if they want to be sure about it, they can measure it again after the local noon time.

After measuring the two lengths (stick length and shadow length) and writing the values on the worksheet, data processing begins. Calculations can be done in the schoolyard, with students working in groups and comparing their results with their classmates. Alternatively, if there is a lack of time, calculations can be done in the classroom at another time. Students can use scientific calculators (or the one on their smartphones) to calculate the angle θ .

Extension activities

There are several extension activities that can be done to make the learning experience more meaningful, such as calculating the radius of the Earth and collaborating with another school. These are described fully in the supporting material.

When doing the calculations and exporting the results, you could use the following questions as the basis for a discussion:

• What could be the measurement errors during the experiment?
• What can be done to minimize errors?
• What errors could have been made by Eratosthenes when he performed his own experiment 2300 years ago? To answer this, the globe could be used, with pins on Alexandria and Syene. Alternatively, students can observe the two cities on Google Earth.
• Angle θ , calculated during the experiment, also represents what?
• If you do the experiment during the summer/winter solstice, what would you change? Explain.
• Why did Eratosthenes make his measurements during the summer solstice? Could he do it on the spring or autumn equinoxes? Explain.

As a conclusion, you can emphasize to your students that science often develops from a simple idea and an inquisitive mind.

[1] Panhellenic Union of Heads of Laboratory Centers of Natural Sciences (Greek language): https://panekfe.gr/eratosthenes/

• Find more teaching resources relating to the Eratosthenes experiment on the eu website.
• Read more about the life and work of Eratosthenes of Cyrene .
• Watch a video about Eratosthenes by Carl Sagan.
• Explore data visualization by sketching graphs from story videos of everyday events: Reuterswärd E (2022) Graphing stories . Science in School 58 .
• Discover how physicists study very small and large objects that cannot be directly observed or measured: Akhobadze K (2021) Exploring the universe: from very small to very large . Science in School 55.
• Get your students to use their smartphones for some hands-on astronomy: Rath G, Jeanjacquot P, Hayes E (2016) Smart measurements of the heavens . Science in School 36: 37–42.
• Challenge your students to solve the mystery box puzzle while learning about the nature of science: Kranjc Horvat A (2022) The mystery box challenge: explore the nature of science .  Science in School 59 .
• Measure distances to the stars like real astronomers with this classroom activity: Pössel M (2017) Finding the scale of space . Science in School 40 : 40–45.
• Measure the distance between Earth and the Moon with the help of radio signals: Middelkoop R (2017) To the Moon and back: reflecting a radio signal to calculate the distance . Science in School 41: 44–48.

Sevasti Malamou is a secondary school physics teacher at the Music School of Ioannina Nikolaos Doumpas, Greece. She has also taught chemistry, biology, and geography and enjoys using innovative methods to teach science. She holds master’s degrees in both electronics and telecommunications, and physics didactics.

Vasilios Kitsakis is a secondary school maths teacher and currently headmaster at the Music School of Ioannina Nikolaos Doumpas, Greece. He holds master’s degrees in studies in education and educational management. He has taken part in training programs and conferences as a speaker.

This article introduces ideas and activities that move teachers and students from a historical concept to its replication using modern technologies.

Marie Walsh, Science Lecturer, Ireland

Supporting materials

Introductory activity

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This measurement is more than 2,200 years old, and its accuracy is remarkable

Topic: Mathematics Education

Ancient mathematicians used their knowledge of geometry to take accurate measurements of earth ( Getty: Aris Messinis )

There are so many negative numbers and statistics flying around at the moment, it's a little overwhelming.

So let me tell you an inspiring story about numbers: it will be a relief to think about something else for a few minutes.

Travel back in time

About 2,250 years ago, there was a man called Eratosthenes.

He was one of those ancient Greeks who changed the world.

He was a polymath, someone with expert knowledge of a range of topics.

A mathematician, geographer, astronomer, philosopher, poet, and music theorist. 

He's famous for being the first person known to have measured the earth's circumference.

How did he do it?

It's surprisingly simple. You just need some basic geometry.

Watch the short clip below of the great Carl Sagan to see how it was done. 

I've set it to play from the 4 min 11 sec mark, because that's where Sagan explains the calculations. But the few minutes before that point are also wonderful.

In case you couldn't watch or hear the video, I'll explain the story quickly.

Around 245 BC, when Eratosthenes was in his 30s, he was working as a librarian in the famous Library of Alexandria in Egypt.

It was there where he read about a water well in the city of Syene (modern-day Aswan in southern Egypt).

At midday every summer solstice, the sun would shine directly down into the well, illuminating the water at the bottom - but casting no shadow on the walls of the well.

It meant the sun sat directly above Syene at that exact moment.

So Eratosthenes wondered, if he stuck a pole in the ground in Alexandria at that same moment, would it cast a shadow?

And it turns out it did.

What did it prove?

His little experiment demonstrated that the surface of the earth was curved like a sphere.

Why? Because his pole in Alexandria was sticking straight into the air but the curvature of the earth made it face slightly away from the sun, causing the pole to throw a small shadow onto the ground.

And that allowed him to do something else.

Since he knew the height of the pole, and the length of the shadow it cast, it meant he knew the lengths of two sides of a right-angled triangle.

That meant he could figure out the length of the third side of the triangle, and he could also figure out the angle at the top of the pole, between the sunbeam and the pole itself.

It was 7.2 degrees.

Therefore, he knew the sun was hitting Alexandria at an angle of 7.2 degrees precisely at midday on the summer solstice.

When a fraction goes a long way

And that left him with one final measurement.

To figure out the circumference of the earth, he needed to somehow measure the distance between Alexandria and Syene.

So he asked someone (or a team of people) to walk it.

Those people were called "bematists", professional surveyors who were trained to measure vast distances extremely accurately by pacing the distance.

They estimated the distance between the two cities was roughly 5,000 stadia (or 800 kilometres).

And that was everything Eratosthenes needed.

He had all the ingredients to calculate the circumference of the earth.

A few assumptions help

Let's go.

Assume the earth is a perfect sphere (it's not, but it's not a problem for these calculations).

We know there are 360 degrees in a circle.

If you cut the earth in half, the earth's great circle will obviously have 360 degrees, and the circumference of that circle (i.e. the total length of its perimeter) could be divided up into equal bits of whatever length.

Eratosthenes knew that the distance between Syene and Alexandria was 7.2 degrees along the surface of the earth.

So how many of those distances would he need to stretch around the entire 360 degree circumference of the earth?

He divided 360 by 7.2, which gave a neat 50.

That meant, given the distance between Alexandria and Syene was 800 kilometres, all he had to do was multiply 800 by 50, which came to 40,000.

And that was it.

The circumference of the earth was 40,000 kilometres, according to Eratosthenes' calculations.

The bematists estimated that Syene was 5,000 stadia (or 800 kilometres) away from Alexandria, which gave Eratosthenes the final number he needed to work out the earth's circumference ( Source: Khan Academy, "Eratosthenes of Cyrene: Measuring the Circumference of the Earth."  )

Was he correct?

He was incredibly close.

As it turns out, the meridional circumference of Earth (from pole to pole) is roughly 40,008 km, and the equatorial circumference is about 40,075 km (it's bigger at the equator because Earth slightly bulges in its middle).

Not bad for someone with such rudimentary tools.

Eratosthenes used his new knowledge to revolutionise map making.

He drew a map of the known world with parallels and meridians, making it possible to estimate real distances between objects, and plotted the names and locations of hundreds of cities over the grid.

It was the beginning of modern geography.

Anyway, I hope that's been a pleasant escape from reality.

When so much attention is focused on the maths of hospitalisations and vaccinations and contagion, it's easy to forget that maths can also be a source of innocent joy.

Take care this week.

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How did Eratosthenes calculate the size of the Earth?

Eratosthenes was born in the country we now call Lybia, but in those days was called Cyrene.

19th century reconstruction of Eratosthenes' map of the known world, c.194 BC. Source: Wikipedia.

Eratosthenes studied in Alexandria and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, the center of science and learning in the ancient world, succeeding to Apollonius of Rhodes, in that post. He was the third chief librarian of the Great Library of Alexandria.

As chief librarian he read many documents and found out that at the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) that is located near the tropic of Cancer on June there is a well where on certain day of the year the sunlight goes down to the bottom of the well. He knew that in Alexandria there was no day that the great Obelisk did not produce shadow and he measured the shadow angle on the day the Sun was directly above the well in Aswan. He needed to know the distance from the well in Aswan to Alexandria and there several different versions of how he found out its value. The most popular one is that he send a slave to measure it in footsteps. The value that he used in his calculations was 8000 stadia (1 egiptian stadium is about 157.5 m, though the exact size of the stadium is often a theme of discussion).

With this information he measured the circumference of the Earth without leaving Egypt by assuming that Earth was a sphere and that the Sun rays are parallel when they arrive to Earth.

Eratosthenes assumed that Earth is a sphere and that the solar rays are parallel when they reach Earth.

If this was true then the angle (α) that the shadow made on the top of the obelisk in Alexandria would be the same as the diffrence in latitude between the two places.

Eratosthenes used a simple formula that relates the proportionality proportionality of distance on the meridian (d) and the difference in latitude (α) to the relation between the perimeter (P) and the angle of the circle (360º):

The shadow angle at the top of the obelisk measured by Eratosthenes was 7.2º, so he calculated that the Earth was about 252 000 stadia.

If we assume the Egyptian stadium this is about 39 817 km (252 808 stadium × 157.5 m/stadium) which has an error of less than 1% when compared to the accepted value of the meridional perimeter of Earth that is 40 007.86 km.

Eratosthenes' experiment was one of the most important experiments in antiquity and his estimate of the earth’s size was accepted for hundreds of years afterwards. It was, in fact, the most accurate estimate until Man was able to go to Space.

© EAAE - European Association for Astronomy Education 2024

September 7, 2017

Measure Earth's Circumference with a Shadow

A geometry science project from Science Buddies

By Science Buddies & Ben Finio

The earth is massive, but you don't need a massive ruler to measure its size. All you need are a few household items--and little bit of geometry!

George Retseck

Key concepts Mathematics Geometry Circumference Angles Earth's equator

Introduction If you wanted to measure the circumference of Earth, how long would your tape measure have to be? Would you need to walk the whole way around the world to find the answer? Do you think you can do it with just a meterstick in one location? Try this project to find out!

Before you begin, however, it is important to note this project will only work within about two weeks of either the spring or fall equinoxes (usually around March 20 and September 23, respectively).

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Background What is Earth’s circumference? In the age of modern technology this may seem like an easy question for scientists to answer with tools such as satellites and GPS—and it would be even easier for you to look up the answer online. It might seem like it would be impossible for you to measure the circumference of our planet using only a meterstick. The Greek mathematician Eratosthenes, however, was able to estimate Earth’s circumference more than 2,000 years ago, without the aid of any modern technology. How? He used a little knowledge about geometry!

At the time Eratosthenes was in the city of Alexandria in Egypt. He read that in a city named Syene south of Alexandria, on a particular day of the year at noon, the sun’s reflection was visible at the bottom of a deep well. This meant the sun had to be directly overhead. (Another way to think about this is that perfectly vertical objects would cast no shadow.) On that same day in Alexandria a vertical object did cast a shadow. Using geometry, he calculated the circumference of Earth based on a few things that he knew (and one he didn’t):

He knew there are 360 degrees in a circle.

He could measure the angle of the shadow cast by a tall object in Alexandria.

He knew the overland distance between Alexandria and Syene. (The two cities were close enough that the distance could be measured on foot.)

The only unknown in the equation is the circumference of Earth!

 The resulting equation was:

Angle of shadow in Alexandria / 360 degrees = Distance between Alexandria and Syene / Circumference of Earth

In this project you will do this calculation yourself by measuring the angle formed by a meterstick’s shadow at your location. You will need to do the test near the fall or spring equinoxes, when the sun is directly overhead at Earth's equator. Then you can look up the distance between your city and the equator and use the same equation Eratosthenes used to calculate Earth’s circumference. How close do you think your result will be to the “real” value?

There is a geometric rule about the angles formed by a line that intersects two parallel lines. Eratosthenes assumed the sun was far enough away from our planet that its rays were effectively parallel when they arrived at Earth. This told him the angle of the shadow he measured in Alexandria was equal to the angle between Alexandria and Syene, measured at Earth’s center. If this sounds confusing, don’t worry! It is much easier to visualize with a picture. See the references in the “More to explore” section for some helpful diagrams and a more detailed explanation of the geometry involved.  

Sunny day on or near the spring or fall equinoxes (about March 20 or September 23, respectively)

Flat, level ground that will be in direct sunlight around noon

Volunteer to help hold the meterstick while you take measurements (Or, if you are doing the test alone, you can use a bucket of sand or dirt to insert one end of the meter stick to hold it upright.)

Stick or rock to mark the location of the shadow

Long piece of string

Optional: plumb bob (you can make one by tying a small weight to the end of a string) or post level to make sure the meter stick is vertical  

Preparation

Look at your local weather forecast a few days in advance and pick a day where it looks like it will be mostly sunny around noon. (You have a window of several weeks to do this project, so don’t get discouraged if it turns out to be cloudy! You can try again.)

Look up the sunrise and sunset times for that day in your local newspaper or on a calendar, weather or astronomy Web site. You will need to calculate “solar noon,” the time exactly halfway between sunrise and sunset, which is when the sun will be directly overhead. This will probably not be exactly 12 o’clock noon.

Go outside and set up for your materials about 10 minutes before solar noon so you have everything ready.  

Set up your meter stick vertically, outside in a sunny spot just before solar noon.

If you have a volunteer to help, have them hold the meterstick. Otherwise, bury one end of the meterstick in a bucket of sand or dirt so it stays upright.

If you have a post level or plumb bob, use it to make sure the meterstick is perfectly vertical. Otherwise, do your best to eyeball it.

At solar noon, mark the end of the meterstick's shadow on the ground with a stick or a rock.

Draw an imaginary line between the top of the meterstick and the tip of its shadow. Your goal is to measure the angle between this line and the meterstick. Have your volunteer stretch a piece of string between the top of the meterstick and the end of its shadow.

Use a protractor to measure the angle between the string and the meterstick in degrees. Write this angle down.

Look up the distance between your city and the equator.

Calculate the circumference of the Earth using this equation:

Circumference = 360 x distance between your city and the equator / angle of shadow that you measured       

What value do you get? How close is your answer to the true circumference of Earth (see “Observations and results” section)?

Extra: Try repeating your test on different days before, on and after the equinox; or at different times before, at and after solar noon. How much does the accuracy of your answer change?

Extra: Ask a friend or family member in a different city to try the test on the same day and compare your results. Do you get the same answer?

Observations and results In 200 B.C. Eratosthenes estimated Earth’s circumference at about 46,250 kilometers (28,735 miles). Today we know our planet's circumference is roughly 40,000 kilometers (24,850 miles). Not bad for a more than 2,000-year-old estimate made with no modern technology! Depending on the error in your measurements—such as the exact day and time you did the test, how accurately you were able to measure the angle or length of the shadow and how accurately you measured the distance between your city and the equator—you should be able to calculate a value fairly close to 40,000 kilometers (within a few hundred or maybe a few thousand). All without leaving your own backyard!

More to explore Calculating the Circumference of the Earth , from Science Buddies Lesson: Measure the Earth's Circumference , from eGFI Angles, Parallel Lines and Transversals , from Math Planet Science Activities for All Ages! , from Science Buddies

This activity brought to you in partnership with Science Buddies

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What were Eratosthenes’ major achievements?

What is eratosthenes famous for.

• Is mathematics a physical science?
• What does Earth look like?
• How is astronomy different from cosmology?

Eratosthenes

Our editors will review what you’ve submitted and determine whether to revise the article.

• APSNews - This Month in Physics History - June, ca. 240 B.C. Eratosthenes Measures the Earth
• Khan Academy - Eratosthenes of Cyrene
• World History Encyclopedia - Eratosthenes
• CORE - Eratosthenes on the “Measurement” of the Earth
• Planet Facts - Biography of Eratosthenes
• Famous Scientists - Biography of Eratosthenes
• Academia - Eratosthenes of Cyrene: Biography & Work as a Mathematician
• Eratosthenes - Student Encyclopedia (Ages 11 and up)

In addition to calculating Earth ’s circumference, Eratosthenes created the Sieve of Eratosthenes (a procedure for finding prime numbers), tried to fix the dates of literary and political events since the siege of Troy , and is thought to have created the armillary sphere (an early astronomical device for representing the great circles of the heavens).

Eratosthenes measured Earth’s circumference mathematically using two surface points to make the calculation. He noted that the Sun’s rays fell vertically at noon in Syene (now Aswān ), Egypt , at the summer solstice . In Alexandria , also in Egypt, at the same date and time, sunlight fell at an angle of about 7.2° from the vertical.

How did Eratosthenes die?

Eratosthenes died in his 80s in Alexandria, Egypt. He had become blind in his old age and could no longer work by 195 BCE. He reportedly fell into despair, and he is said to have committed suicide by voluntary starvation in 194 as a result.

Eratosthenes (born c. 276 bce , Cyrene , Libya—died c. 194 bce , Alexandria , Egypt) was a Greek scientific writer, astronomer, and poet, who made the first measurement of the size of Earth for which any details are known.

At Syene (now Aswān), some 800 km (500 miles) southeast of Alexandria in Egypt , the Sun’s rays fall vertically at noon at the summer solstice . Eratosthenes noted that at Alexandria, at the same date and time, sunlight fell at an angle of about 7.2° from the vertical. (Writing before the Greeks adopted the degree, a Babylonian unit of measure, he actually said “a fiftieth of a circle.”) He correctly assumed the Sun’s distance to be very great; its rays therefore are practically parallel when they reach Earth. Given an estimate of the distance between the two cities, he was able to calculate the circumference of Earth, obtaining 250,000 stadia. Earlier estimates of the circumference of Earth had been made (for example, Aristotle says that “some mathematicians” had obtained a value of 400,000 stadia), but no details of their methods have survived. An account of Eratosthenes’ method is preserved in the Greek astronomer Cleomedes’ Meteora . The exact length of the units (stadia) he used is doubtful, and the accuracy of his result is therefore uncertain. His measurement of Earth’s circumference may have varied by 0.5 to 17 percent from the value accepted by modern astronomers, but it was certainly in the right range. He also measured the degree of obliquity of the ecliptic (in effect, the tilt of Earth’s axis) and wrote a treatise on the octaëteris , an eight-year lunar-solar cycle. He is credited with devising an algorithm for finding prime numbers called the sieve of Eratosthenes , in which one arranges the natural numbers in numerical order and strikes out one, every second number following two, every third number following three, and so on, which just leaves the prime numbers.

Eratosthenes’ only surviving work is Catasterisms , a book about the constellations , which gives a description and story for each constellation , as well as a count of the number of stars contained in it, but the attribution of this work has been doubted by some scholars. His mathematical work is known principally from the writings of the Greek geometer Pappus of Alexandria , and his geographical work from the first two books of the Geography of the Greek geographer Strabo .

After study in Alexandria and Athens, Eratosthenes settled in Alexandria about 255 bce and became director of the great library there. He tried to fix the dates of literary and political events since the siege of Troy . His writings included a poem inspired by astronomy , as well as works on the theatre and on ethics . Eratosthenes was afflicted by blindness in his old age , and he is said to have committed suicide by voluntary starvation.

How Did Eratosthene Calculate The Circumference Of Earth In 240 BC?

The problem, the man for the job, the estimation, the advantages.

Eratosthene calculated the circumference of Earth by measuring the length of a stick’s shadow in Alexandria and the distance between Alexandria and Syrene on foot. He then took the inverse tangent of the ratio between the shadow’s length and the stick’s length to find the angle of inclination of the Sun. He calculated the total circumference of the Earth to be ((360/7.2) x D ) kilometers, with D being the distance between Alexandria and Syrene.

This might come as a surprise for our younger readers, but throughout history, not everything that people learnt could be found on the Internet. Before that, humans “wasted” time poring over books, and before books, our ancestors had to communicate knowledge verbally! With that in mind, how is it possible that someone could accurately predict the circumference of the Earth without ever using a computer?

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Ancient astronomy was a puzzling field, with men using only visual observations, rather than the help of complex instruments. Even if they did have the intellectual prowess to tackle certain problems, most early scientists had to battle social and religious conventions. The idea of a spherical Earth appeared in Greek philosophy from Pythagoras in the 6th century BC and was sneered at because until then, Earth was considered completely flat! Aristotle provided evidence for the spherical shape of the Earth on empirical grounds by 330 BC, which is very slow progress when you think about it.

The problem with determining the Earth’s circumference held no importance if the Earth was flat, but gradually, once people started to acknowledge the actual shape, they needed to know exactly how big our world truly was. The only tool that astronomers had in 300 BC was their ability to recognize patterns.

Also Read: How Did People Figure Out That The Earth Was Round Without Any Technology?

Eratosthene was a Greek mathematician and the chief librarian at the Library of Alexandria. He is also credited for inventing the discipline of geography. His method for determining the size of the Earth was an elegant application of simple geometry to an otherwise very difficult problem. Although he took some small liberties with facts and made a number of assumptions, his calculations were pretty accurate. What’s even more amazing is the fact that this epic calculation took him a negligible amount of time, given that all his calculations could be done by hand using simple trigonometry.

Also Read: How Do We Know The Mass Of The Earth?

Eratosthenes knew that the Sun was directly overhead in the town of Syrene, in southern Egypt, on the Summer Solstice. Since the Sun was directly overhead, a well situated in that town didn’t cast a shadow at its bottom. He also knew that his hometown of Alexandria was further north of Syrene, and the exact distance on foot between the two cities was easily determined.

Next, he measured the length of a tall stick called a ‘gnomon’ and stuck it in the ground in Alexandria. When the sun’s rays struck the gnomon, it cast a shadow. Because the sun was directly overhead in Syrene, it had to be obliquely tilted if observed from Alexandria. Hence, a shadow of the stick could be observed in the latter town.

The length of the shadow and the actual length of the stick allowed Eratosthenes to calculate the angle of inclination of the Sun. This can be done by taking the inverse tangent of the ratio between the shadow’s length and the stick’s length.

The angle labelled “A” is shown in the illustration above. By simple rules of geometry, it can also be observed that A is the angle subtended from the center of the Earth by the distance between the two cities. This angle was found to be nearly 7.2 degrees.

Now that Eratosthenes knew the subtended angle and the actual distance between the two cities of Syrene and Alexandria, he could calculate the total circumference of the Earth. The concept he used was very simple.

Distance between Alexandria and Syrene = D kilometers

Angle subtended by them on the center of the Earth= 7.2 degrees

Total angle of a circle= 360 degrees

Total Circumference of the Earth= ((360/7.2) x D ) kilometers

The unit of measurement that was popular in Greece at the time was stadia. Historians have yet to figure out the true length of a single stadia, but popular estimates put it around 160 meters. Eratosthenes estimated the circumference to be 252,000 stades, which is approximately 40,074 kilometers.

Shockingly enough… the real polar circumference is only 66 kilometers greater than this estimate!

The few assumptions that Eratosthenes made were trivial, but they need to be mentioned anyway. He assumed that the Sun was sufficiently far away from the Earth, so that its rays were always falling in parallel at the two cities. However, in reality, the rays at Syrene and Alexandria are ever so slightly inclined. Another liberty that he took was assuming that the distance between Syrene and Alexandria was very small, as compared to the circumference of the Earth, so it could be treated as a flat surface, rather than the arc of a larger circle. Needless to say, the Earth isn’t a perfect sphere and the two cities do not lie on the same latitude. Although the calculation is slightly flawed, this primitive technique provided an answer with only a 0.16% error, which is rather phenomenal!

Firstly, it was of paramount importance for us to find out how big our home actually was! Geographical research improved by leaps and bound following this determination. Through the study of eclipses, the size of the moon and the Sun was also easier to estimate, since we knew how big of a shadow the Earth cast, relative to its size. We even had a better understanding of seasons and their predictability.

Christopher Columbus studied what Eratosthenes had written about the size of the earth, but instead chose to believe another geographer named Toscanelli, who calculated the Earth’s circumference and came up with a result roughly 33% smaller than the actual value. Had Columbus set sail believing that Eratosthenes’ larger circumference value was more accurate, he would have known that the place he made landfall was not Asia, but rather the real New World, now known as America!

• Eratosthenes - www.astro.cornell.edu:80
• Astronomy 101 Specials: Eratosthenes and the Size of the Earth. Bucknell University
• Eratosthenes Earth Measurement. umich.edu

Harsh Gupta graduated from IIT Bombay, India with a Bachelors degree in Chemical Engineering. His pedantic and ‘know-it-all’ nature made it impossible for him not to spread knowledge about (hopefully) interesting topics. He likes movies, music and does not shy away from talking and writing about that too.

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Some 1,700 years before the famous expedition of Magellan and Elcano, which took more than three years to circumnavigate the Earth to verify that it is not flat, but round, the Greek polymath Eratosthenes managed to make that same finding and also estimate its diameter with a straight-forward piece of mathematical reasoning, without leaving the city of Alexandria and with surprising accuracy. The power of the mathematics developed by the classical Greeks was the key to performing this remarkable feat and managing to measure the impossible.

Eratosthenes was born in Cyrene, a city located in modern-day Libya, around 276 B.C. and in the year 236 B.C. became Chief Librarian of the prestigious Library of Alexandria . He made contributions in fields as apparently disparate as poetry, philosophy, mathematics, astronomy, history and geography, among others. As a mathematician, he is well known for the so-called Sieve of Eratosthenes , which makes it possible to isolate and determine all prime numbers up to a given natural number and which is still used today.

In addition, he knew how to apply basic mathematical knowledge, such as the calculation of the length of an arc of circumference—which is now studied in secondary school—in order to approximate the radius of the Earth very precisely, using only rudimentary instruments. In particular, Eratosthenes observed the shadow produced by the rays of the Sun during the summer solstice in two places far enough away from each other: Siena (now the Egyptian city of Aswan) and Alexandria, located north of Siena following the same meridian.

In the solar noon of that day, in a deep well of Siena, one could see for a very brief instant the reflection of the water it contained, which showed that the rays of the sun fell perpendicularly. This is true at the time of the summer solstice and on the Tropic of Cance (Eratosthenes placed Siena on that terrestrial parallel) However, at that same moment, in Alexandria (located about 7 degrees farther north) the rays fell at a slightly transversal angle, since obelisks or a simple cane stuck in the ground cast a small but perceptible shadow . This is already in itself a simple proof that the Earth cannot be flat, because if it were so, at that same moment in Alexandria the solar rays should also have fallen perpendicularly and not provided any shade.

A simple rule of three

Eratosthenes started from a model of a round Earth in the shape of a sphere, so he knew that the curvature of the Earth would cause this effect. He devised a method to calculate the diameter of the sphere from only two data points : the angle of incidence of the sun in Alexandria on the summer solstice (which is the same as the section of the circumference defined by the two cities) and the distance between them. In this way, with a simple rule of three he could calculate the length of the circumference of the Earth. If the angle of incidence gives rise to a length of an arc of circumference equal to the distance between Alexandria and Siena, then the total length will correspond to 360 degrees (the full circumference).

To calculate the angle of incidence of the sun’s rays in Alexandria on the summer solstice he had to use trigonometry concepts, which were already known to Greek mathematicians, although using methods very different from those used today. In current terminology, that angle of incidence is the value of the arctangent of the division between the shadow of an object and its height (see Figure 2). Eratosthenes obtained a value close to 7.2 degrees , or 1/50th the circumference of a circle.

To finish his calculation he needed a sufficiently accurate estimate of the distance between the two cities. Legend has it that Eratosthenes knew that a camel took fifty days to get from one city to another, traveling about a hundred stadia per day, so he estimated the distance at about five thousand stadia. The precision of his calculation is unknown, since the stadium is not a unit of measurement with a clear value. But if we consider as a measure of a stadium the one corresponding to the Egyptian stadium (157.5 metres), we would obtain an approximate distance of 787.5 km. Substituting these values ​​in the rule of three above, we obtain a circumference length of 39,375 km . This is an excellent approximation of the actual value, which is about 40,075 km at the equator.

A model of the Earth that was quite successful

Eratosthenes had a model of the Earth and the solar system that was quite successful. Even though he made a series of assumptions that are not entirely accurate ( the Earth is not a sphere, the sun’s rays are not parallel, Siena is not directly on the Tropic of Cancer …), by combining modern capabilities with this same technique, a result extremely close to the real one can be obtained. Nowadays, this value is estimated using satellites and geolocation systems. These precise measurements allow us to detect even small modifications (of centimetres) on the surface of the Earth.

However, many centuries before, with hardly any technology, using the ingenuity and mathematics developed by their predecessors (Pythagoras, Archimedes, Euclid, Thales of Miletus…), other classical Greeks made amazing calculations, such as calculating the distance from the Earth to the Sun, predicting eclipses and the movement of known planets, and even proposing that the Sun was the centre of the Universe and not the Earth, as did Aristarchus of Samos. With these advances, they went beyond experimental knowledge, based only on direct measurements, to a much more ambitious conception of scientific knowledge, which allowed us to know things beyond our own immediate perception.

David Martín de Diego and Ágata Timón

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Eratosthenes (276 BC-194 BC) was a Greek mathematician, geographer and astronomer. He was born in Cyrene (now Libya) and died in Ptolemaic Alexandria. He is noted for devising a map system based on latitude and longitude lines and computing the size of the Earth. Eratosthenes studied at Alexandria and for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library. He made several important contributions to mathematics and science, and was a good friend to . Around 255 BC he invented the (an astronomical instrument for determining celestial positions), which was widely used until the invention of the in the 18th century. Circa 200 BC Eratosthenes is thought to have coined or to have adopted the word geography, the descriptive study of the Earth. Eratosthenes' other contributions include: with an angle error of 7'. Before we begin a few definitions: Tropic of Cancer - is one of five major circles of latitude that mark maps of the Earth. The Tropic of Cancer currently latitude is 23° 26′ 22″ north of the Equator. Local noon is when the sun is the highest in the sky and can be quite different from 12:00 noon on the clock. Solstice - is an astronomical event that happens twice each year, when the tilt of the Earth's axis is most inclined toward or away from the Sun. In the northern hemisphere, the maximum inclination toward the sun is around 21 June (the summer solstice) and with the maximum inclination away around 21 December (the winter solstice). For the southern hemisphere winter and summer solstices are exchanged. What matters for our experiment is the fact that on the summer solstice, local noon, the sun rays are just overhead (at a right angle to the ground) on the Tropic of Cancer. Repeat Eratosthenes' Experiment from on . Eratosthenes measured, at his local noon in Alexandria, the angle of elevation of the sun on the summer solstice (21 June). Eratosthenes used the local noon and no other time of the day since at local noon all relevant places and sunrays are placed on the same imaginary plane enabling the use of simple geometry for his calculations. In order to repeat Eratosthenes’ experiment you’ll have to do the same. First, calculate your local noon because it may be quite different from 12:00 noon on the clock. There are several ways to compute its exact occurrence. Basically, local noon is half-way between sunrise and sunset. You can obtain sunrise and sunset times, for June 21, from your local paper or from this link: http://aa.usno.navy.mil... which also calculates local noon (sun transit). You can also obtain it by yourself by using a sundial or find out when the shadow is the shortest around noon time. On June 21 erect a vertical straight stick or pole of about 1 meter using a carpenter’s level and measure the length of the shadow it casts at your local noon. With simple trigonometry you can obtain the angle of the elevation of the sun. You can also obtain the angle, without trigonometry, by drawing the stick and shadow proportionally and measuring it with a protractor. You can compare your results with a web based applet like this: http://www.jgiesen.de/azimuth but be careful to use it correctly (insert your correct time zone, local noon, coordinates, date and ensure that the dropdown menu points to elevation). After you get the angle of sun elevation, it’s very easy to calculate the zenith angle by subtracting it from 90°, like Eratosthenes did. Now you’ll have to measure the distance from your location to the Tropic of Cancer latitude line - not by camel caravans of course, the Eratosthenes way. You can use a relatively large scale map, but take in account that maps tend to distort distance and the best option is to use a globe. The distance from your location to the Tropic of Cancer should be measured from north to south. In other words the distance line has to cut the Tropic of Cancer at a right angle. There are also web based calculators for this: https://web.archive.org... . Now it's easy to calculate the Earth circumference by using the following formula: Likewise, you can also perform this experiment on the winter solstice that takes place around 21 December, but you’ll have to measure your distance from the Tropic of Capricorn instead from the Tropic of Cancer because on this date the sun reaches its highest degree of elevation on the Tropic of Capricorn (23° 26′ 22″ south of the Equator). It is also possible to perform this experiment on the two Equinoxes which occur on 20 March and 23 September each year when the sun is crossing the equator at the local noon on those dates and the sun rays are just overhead the equator at a right angle to the ground. But instead to measure your distance from the Tropic of Cancer or the Tropic of Capricorn you’ll have to measure it from the equator. There is another option and you can perform this experiment on any other date of the year, at local noon time, but you should have some partner located on your longitude willing to measure sun elevation at the same time. Take in account that you'll have to be a little careful treating correctly the sun angles obtained in this case. At any date the sun reaches its highest position, at noon time, at some latitude. From here is clear that if the two places involved are located on the same side of this latitude (north or south) the shadows will be casted at the same direction and the obtained angles should be subtracted from each other, whereas if the places are located on different sides of this latitude the shadows will be casted at different directions (southward or northward) and the angles should be added up. Further Reading Discovering the size of the Earth: The Eratosthenes experiment by Angelos Alexopoulos | 15/03/2023 | Blog Get ready to take your students on a journey back in time to the ancient world of Greece, where a brilliant scholar made a groundbreaking discovery that would change the course of history forever. In 240 BC, Eratosthenes of Cyrene, a Greek polymath and chief librarian at the Library of Alexandria, accomplished what no one before him had been able to do – he measured the circumference of the Earth! This remarkable feat was achieved through an inquiry-based activity that involved keen observation, critical thinking, and precise calculations. Back then, the ancient Greeks knew that the Earth was round, but they had no idea about its size. Eratosthenes’ ingenious experiment involved observing the sun’s angle at noon on the summer solstice in two different cities – Syene and Alexandria – which were located at the same longitude. He noticed that at noon on the summer solstice, the sun was directly overhead of a well in Syene, without casting any shadows, while in Alexandria, a stick cast a shadow at the same time, making an angle of about 7.2 degrees. Using this information and the distance between the two cities, Eratosthenes was able to calculate the Earth’s circumference with an impressive degree of accuracy, within 15% of today’s measured values. This milestone discovery not only proved that the Earth was much larger than previously thought but also paved the way for future scientific discoveries. Fast forward 2250 years and Eratosthenes’ experiment remains one of the most beautiful and insightful experiments in the history of science. It is also an exemplary inquiry-based activity that can help introduce students to the scientific way of thinking. By recreating Eratosthenes’ experiment in the classroom, students can learn about the power of observation, critical thinking, and mathematical reasoning. Carl Sagan explains… Watch this video where Carl Sagan explains this monumental experiment. Want to take your students on an exciting journey through time and space, and inspire the next generation of scientists and researchers with the Eratosthenes Experiment? Take part in the international photo contest led by Ellinogermaniki Agogi. Hurry up!   The deadline for submitting your photo is 10 April 2023 . Thunderstorms to Alternate With Heat Wave in Greece Over 140 cyberattacks targeting olympics reported in france, when alain delon flirted with famous greek actress tzeni karezi, locals on greece’s tilos save 50-day-old refugee baby. Environment How an Ancient Greek Calculated the Earth’s Circumference Ancient Greeks made some of the most impressive astronomical discoveries in history, including Eratosthenes’ calculation of the circumference of the Earth. It wasn’t until the mid-20th century that we managed to launch satellites into space and determine the exact kilometers of the circumference of the Earth : 40,030.2 kilometers. But how, then, could the ancient Greek mathematician, Eratosthenes, manage to find pretty much the exact same number without having any pictures of Earth from space or even proper measuring tools? Amazingly, Eratosthenes didn’t have much more than a stick and his brain when he made the amazing discovery. How Eratosthenes discovered the circumference of the Earth Born in Cyrene, an ancient Greek colony in modern-day Libya in 276 BC, Eratosthenes was a polymath, meaning that he had vast knowledge of many different subjects, including mathematics, astronomy, music theory, and poetry. Over two thousand years ago, Eratosthenes heard that in Syene, a town south of Alexandria in Egypt, no vertical shadows were cast at noon on the summer solstice, as the sun was directly overhead. The Greek mathematician wondered if this was the case in Alexandria, too, a few hundreds of miles to the north of Syene. He decided to conduct an experiment. On June 21st, he went to Alexandria and put a stick directly in the ground and waited to see if a shadow would be cast at noon. It turns out there was one, and he tried to measure it. The shadow cast measured to about seven degrees. After conducting the experiment, Eratosthenes came to a very logical conclusion that if the sun’s rays are coming in at the same angle at the same time of day and a stick in Alexandria casts a shadow of seven degrees while the stick in Syene does not cast a shadow at all, it must mean that the Earth’s surface is curved. Carl Sagan, the American astronomer, author, and science communicator was renowned for making difficult scientific concepts understandable to the millions; he did exactly this at the beginning of his renowned series Cosmos by explaining the thought process of Eratosthenes. His calculation The idea of a spherical Earth was already known by Pythagoras around 500 BC and validated by Aristotle a few centuries later. If the Ancient Greeks before him were right, and the Earth was a sphere, Eratosthenes could use his observations to calculate the circumference of our planet. After hiring a man to pace the distance between Syene and Alexandria, he found out that the two cities were five thousand stadia apart, which is about eight hundred kilometers. He could then use simple proportions to find the Earth’s circumference—7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers. And just like that, an ancient Greek calculated precisely the circumference of our entire planet with just a stick and his brain over two thousand years ago. Eratosthenes accomplished many feats throughout his life, including the creation of a chronology of Greek history, an algorithm to find every prime number, and the first global projection of the Earth. See all the latest news from Greece and the world at Greekreporter.com . Contact our newsroom to report an update or send your story, photos and videos. Follow GR on Google News and subscribe here to our daily email! Circumference Eratosthenes mathematician More Greek News The problem with sending people to mars, rare earth metals: the next gold rush to challenge china, us screenings for leon logothetis’ celebrated kindness documentary. Privacy Policy Greek Name Days Watch Greek TV Live © Copyright - GreekReporter.com June, ca. 240 B.C. Eratosthenes Measures the Earth By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes devised a clever method of estimating its circumference. It was around 500 B.C. that Pythagoras first proposed a spherical Earth, mainly on aesthetic grounds rather than on any physical evidence. Like many Greeks, he believed the sphere was the most perfect shape. Possibly the first to propose a spherical Earth based on actual physical evidence was Aristotle (384-322 B.C.), who listed several arguments for a spherical Earth: ships disappear hull first when they sail over the horizon, Earth casts a round shadow on the moon during a lunar eclipse, and different constellations are visible at different latitudes. Around this time Greek philosophers had begun to believe the world could be explained by natural processes rather than invoking the gods, and early astronomers began making physical measurements, in part to better predict the seasons. The first person to determine the size of Earth was Eratosthenes of Cyrene, who produced a surprisingly good measurement using a simple scheme that combined geometrical calculations with physical observations. Eratosthenes was born around 276 B.C., in the region now known as Shahhat, Libya. He studied in Athens at the Lyceum. Around 240 B.C., King Ptolemy III of Alexandria appointed him chief librarian of the library of Alexandria. Known as one of the foremost scholars of the time, Eratosthenes produced impressive works in astronomy, mathematics, geography, philosophy, and poetry. His contemporaries gave him the nickname “Beta” because he was very good, though not quite first-rate, in all these areas of scholarship. Eratosthenes was especially proud of his solution to the problem of doubling a cube, and is now well known for developing the sieve of Eratosthenes, a method of finding prime numbers. Eratosthenes’ most famous accomplishment is his measurement of the circumference of Earth. He recorded the details of this measurement in a manuscript that is now lost, but his technique has been described by other Greek historians and writers. Eratosthenes was fascinated with geography and planned to make a map of the entire world. He realized he needed to know the size of Earth. Obviously, one couldn’t walk all the way around to figure it out. Eratosthenes had heard from travelers about a well in Syene (now Aswan, Egypt) with an interesting property: at noon on the summer solstice, which occurs about June 21 every year, the sun illuminated the entire bottom of this well, without casting any shadows, indicating that the sun was directly overhead. Eratosthenes then measured the angle of a shadow cast by a stick at noon on the summer solstice in Alexandria, and found it made an angle of about 7.2 degrees, or about 1/50 of a complete circle. He realized that if he knew the distance from Alexandria to Syene, he could easily calculate the circumference of Earth. But in those days it was extremely difficult to determine distance with any accuracy. Some distances between cities were measured by the time it took a camel caravan to travel from one city to the other. But camels have a tendency to wander and to walk at varying speeds. So Eratosthenes hired bematists, professional surveyors trained to walk with equal length steps. They found that Syene lies about 5000 stadia from Alexandria. Eratosthenes then used this to calculate the circumference of the Earth to be about 250,000 stadia. Modern scholars disagree about the length of the stadium used by Eratosthenes. Values between 500 and about 600 feet have been suggested, putting Eratosthenes’ calculated circumference between about 24,000 miles and about 29,000 miles. The Earth is now known to measure about 24,900 miles around the equator, slightly less around the poles. Eratosthenes had made the assumption that the sun was so far away that its rays were essentially parallel, that Alexandria is due north of Syene, and that Syene is exactly on the tropic of cancer. While not exactly correct, these assumptions are good enough to make a quite accurate measurement using Eratosthenes’ method. His basic method is sound, and is even used by schoolchildren around the world today. Other Greek scholars repeated the feat of measuring the Earth using a procedure similar to Eratosthenes’ method. Several decades after Eratosthenes measurement, Posidonius used the star Canopus as his light source and the cities of Rhodes and Alexandria as his baseline. But because he had an incorrect value for the distance between Rhodes and Alexandria, he came up with a value for Earth’s circumference of about 18,000 miles, nearly 7,000 miles too small. Ptolemy included this smaller value in his treatise on geography in the second century A.D. Later explorers, including Christopher Columbus, believed Ptolemy’s value and became convinced that Earth was small enough to sail around. If Columbus had instead known Eratosthenes larger, and more accurate, value, perhaps he might never have set sail. Alan Chodos Alan Chodos is the former editor of APS News. 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Upvote Button navigates to signup page Downvote Button navigates to signup page Flag Button navigates to signup page Video transcript Eratosthenes Server costs fundraiser 2024. Eratosthenes (l. c. 276-195 BCE) was a Greek astronomer, geographer, mathematician, and poet best known for being the first to calculate the circumference of the earth and its axial tilt. He is also recognized for his mathematical innovation, the Sieve of Eratosthenes, which identified prime numbers, and his position as head of the Library at Alexandria . He was a native of Cyrene , North Africa (modern-day Shahhat, Libya), a prosperous Greek center of trade on the coast of the Mediterranean Sea. As a young man, he was sent to study in Athens at Plato 's Academy under Arcesilaus (l. c. 316-240 BCE) who had instituted the system of Academic Skepticism at the school. Academic Skepticism encouraged people to question what constituted "knowledge" and to test accepted conclusions about the world themselves rather than repeating what others had claimed as truth. This course of study is thought to have influenced Eratosthenes' later work. He was called to Alexandria, Egypt by Ptolemy III Euergetes (r. 246-222 BCE) as head curator of the famous library there. Eratosthenes remained in Alexandria for the rest of his life, and it was there he made his calculations regarding the circumference of the earth and wrote his best-known works, including a three-volume set on geography credited with coining that term. He was a friend of the inventor and mathematician Archimedes (287-212 BCE) and the two encouraged each other's work. Whereas Archimedes focused on physics, astronomy, and engineering innovations, Eratosthenes engaged with everything that interested him. This earned him the nickname Beta (second letter of the Greek alphabet ) for being second-best at everything though, at the same time, he was praised as highly as an Olympian victor for his various works. In his eighties, he began to lose his eyesight and, feeling he had no reason to live any longer, starved himself to death . He is remembered as one of the greatest polymaths of antiquity and many of the conclusions he reached and terms he coined are still used today. Early Life & Education Eratosthenes was born, the son of one Aglaos, in Cyrene which had been established as a Greek colony in North Africa in 631 BCE. It quickly became a prosperous port of trade, establishing itself as a republic by the mid-5th century BCE, until it was taken by Alexander the Great . After Alexander 's death in 323 BCE, it was ruled by the Ptolemaic Dynasty of Egypt and, in the year of Eratosthenes' birth, declared its independence. It was brought back under Ptolemaic control in 246 BCE by Ptolemy III, when Eratosthenes was still in Athens where his father had sent him to receive an education. Athens, at that time, was the intellectual center of the Mediterranean and Plato's Academy one of the most prestigious educational institutions. Eratosthenes studied under Arcesilaus, a Skeptic philosopher, who encouraged the philosophical discipline of Skepticism first articulated by Pyrrho of Elis (l. c. 360 to c. 270 BCE). Pyrrho wrote nothing himself, but his system was preserved by his student Timon of Phlius (l. c. 320 to c. 235 BCE) and developed by others until Arcesilaus instituted its tenets as the guiding principle of the Academy. Pyrrho's philosophy maintained that people were troubled in life by trusting sense perceptions and believing that conclusions based upon them constituted reality. It is unclear whether Pyrrho claimed that objective reality was unknowable or simply that humans lacked the capacity to know it but, either way, the practical outcome was the same: one's sense perceptions were incapable of rendering the truth about observable phenomena and so, to achieve peace of mind, one should keep from making any judgments or coming to any firm conclusions regarding the sensible world. The best one could do, Pyrrho would suggest, was to remain uncommitted to any kind of conclusion, balancing reasons for and against accepting it equally, and leaving it at that. By doing so, one would achieve a state of mind known as ataraxia, freedom from psychological distress and personal upset. By the time of Arcesilaus, Pyrrho's philosophy had developed to center on the claim that knowledge was impossible because humans were incapable of apprehending the sensible world through sense perceptions. Since one could not know what one did not know, and what one did know was limited to unreliable sense perceptions, one would never be able to find out what one did not know or whether what one knew was, in fact, true. Eratosthenes & Skepticism There is no record of Eratosthenes' time in Athens or what he would have studied but he would have been exposed to this philosophical model at the Academy. Although he is not regarded as a skeptic philosopher, his later work suggests he followed the essential skeptic paradigm of refusing to accept the conclusions of others, rejecting the impressions of sense perceptions, and attempting to find the truth about any given subject through reasoned applications. The later skeptic philosopher and compiler, Sextus Empiricus (l. c. 160 to c. 210 CE) defines the skeptic principles which seem to have informed Eratosthenes' views and methodology: The originating cause of skepticism is, we say, the hope of attaining quietude. Men of talent, who were perturbed by the contradictions in things and in doubt as to which of the alternatives they ought to accept, were led on to inquire what is true in things and what is false, hoping by the settlement of this question to attain quietude. The main basic principle of the skeptic system is that of opposing to every proposition an equal proposition; for we believe that as a consequence of this we end by ceasing to dogmatize. (I.VI.12) Accepting dogmas as truths, skepticism claimed, locked one into an established mindset which one then felt compelled to defend instead of question. By remaining skeptical of all dogma, one was free to explore the subject matter on one's own through reason. By pursuing this course, one might still not come to know what one did not know but would at least know that what one knew could be considered accurate. This seems to have been the model that influenced Eratosthenes' inquiries into accepted knowledge of his time. While still living and studying in Athens, Eratosthenes wrote a number of works, now lost, which were cited by later writers and suggest an application of skeptic principles. Among these was a series of histories, the Chronographies, recalculating important dates in history beginning with the Trojan War , which was highly regarded as more accurate than previous works. Another of his works dealt with the mathematical aspects of Plato's philosophy, possibly demonstrating how philosophical claims could be proven mathematically, though this is speculation as the work has been lost. These works, and others, were brought to the attention of Ptolemy III Euergetes who requested he come to Alexandria to take over the operation of the library. Alexandria & the Circumference of Earth The Ptolemies were interested in making Alexandria the rival of Athens as an intellectual center and, to that end, had already built the library there close to the great temple of the god Serapis (the Serapeum). The Great Library at Alexandria, containing thousands of scrolls, was supplemented by a second in the Serapeum as Ptolemy III made the acquisition of books a priority. Every ship arriving at Alexandria's port was boarded and searched for books. Once found, they were copied, and the copies were returned to their owners; the originals became part of Alexandria's collection. It is said that these copies were so precise that one could not tell them apart from the originals. Eratosthenes, as head librarian, was responsible for the acquisition of these books and the quality of the copies and was also tutor to Ptolemy III's children. He took the Ptolemaic vision of Alexandria as a great seat of learning seriously, expanding the library's collection and organizing it into more clearly defined sections. While going about his various duties, he heard of a well in the city of Syene (modern-day Aswan) to the south whose water (not the sides of the well) was fully illuminated by the sun at noon on the summer solstice (around 21 June), suggesting the sun was directly overhead. He observed that, on the same day, obelisks and other objects in Alexandria cast long shadows and understood that, by calculating the distance between the two cities and the angle of the sun, he could find the circumference of the earth. In c. 240 BCE, he erected a pole at Alexandria and hired a man to walk the distance from Alexandria to Syene to measure the distance (though it was already known from trade caravans). Once he knew the distance was 5,000 stadia (500 miles/800 km), he measured the angle of the sun's rays by this pole (dividing the length of the shadow by the height of the pole) for an angle of 7.12 degrees. The Greeks already knew the earth was round and regarded it as a circle of 360 degrees and so by dividing 360 by 7.2 (so that 360 would divide evenly) he arrived at a circumference for the earth of 250.000 stades (approximately 24,854 miles/40,000 km). Eratosthenes published his conclusions in his On the Measure of the Earth which only exists today as fragments in the works of other writers, beginning with the astronomer Cleomedes whose text is the basis for those that followed. His calculations were generally accepted as accurate and the geographer Strabo (l. 64 BCE to c. 24 CE), in his Geography , notes that, while this was not true of everyone later on, Eratosthenes' calculations continued to be regarded as sound and were still in use at the time of the astronomer Hipparchus of Nicea (190-120 BCE): Sign up for our free weekly email newsletter! Now, his introduction of the principles of mathematics and physics into the subject [of geography] is a commendable thing; also his remark that if the earth is sphere-shaped, just as the universe is, it is inhabited all the way round; and his other remarks of this nature [as well]. But as to the question whether the earth is as large as he has said, later writers do not agree with him; neither do they approve his measurement of the earth. Still, when Hipparchus plots the celestial phenomena for the several inhabited places, he uses, in addition, those intervals measured by Eratosthenes on the meridian through Meroe and Alexandria and the Borysthenes, after saying that they deviate but slightly from the truth. (Book I.4.1) Strabo was commenting here on Eratosthenes' 3-Volume work Geography which sought to accurately map and chart the world. His first volume criticized Homer 's Odyssey as geographically absurd in that the various lands Odysseus is said to have visited were much closer to each other than depicted. This volume also coined the term geography and provided an introduction to the subject. The second volume contained, among other observations, the steps he took in calculating the circumference of the earth, and the third volume is said to have detailed the various inhabited lands and commented on the peoples found there. Strabo, in commenting on the work, notes how Eratosthenes objects to the Greek sense of superiority over others, claiming all people should be judged on individual merits, not by race, ethnicity, or nationality: Now, towards the end of his treatise – after withholding praise from those who divide the whole multitude of mankind into two groups, namely, Greeks and Barbarians, and also from those who advised Alexander to treat the Greeks as friends but the Barbarians as enemies – Eratosthenes goes on to say that it would be better to make such divisions according to good qualities and bad qualities; for not only are many of the Greeks bad, but many of the Barbarians are refined. (Book I.4.9) Eratosthenes' Geography , like his other works, is also lost but was considered a significant intellectual achievement in antiquity as well as controversial since it challenged the Homeric view of the world which many claimed as irrefutable truth. In keeping with his skeptical education, however, Eratosthenes refused to accept the popular understanding of any subject and sought always to find out the truth of a matter for himself. Sieve of Eratosthenes An example of this is his algorithm known as the Sieve of Eratosthenes which located prime numbers. A prime number is any natural number that is not reached by combining two smaller numbers while a composite number is the product of any given smaller amounts. The Greeks did not define the number 1 even as a number and so the number 2 was understood as the first prime number. The Sieve of Eratosthenes was so-called because it acted like a sieve to separate prime numbers from composite numbers. Beginning with the number 2, the multiples of composite numbers are sequentially revealed until all that is left in the “sieve” are prime numbers. This innovation assisted in easier and more efficient mathematical calculations. He is also said to have written works on drama and the theater in general, ethics, astronomy, and to have mapped the Nile River further and more accurately than anyone before him. He was also known to have created a calendar which accounted for leap years, but these contributions have all been lost. Scholar T. L. Heath comments: In the work On the Measurement of the Earth , Eratosthenes is said to have discussed other astronomical matters, the distance of the tropic and polar circles, the sizes and distances of the sun and moon, total and partial eclipses, etc. (Livingstone, 127) A true polymath, Eratosthenes is said to have contributed significantly to many different subject areas and disciplines before his failing eyesight led him to take his own life. Although he is said to have been given the nickname Beta – the equivalent of the phrase "jack of all trades, master of none" in the present day – his reputation for excellence in many different fields suggests this was more of a joke than anything to be taken seriously. Though his work was highly regarded, it was still challenged and his calculations for the circumference of the earth were reworked by the later astronomer Posidonius of Rhodes (l. c. 135 to c. 51 BCE). Posidonius' system was considered easier to use and was closer to the dimensions proposed by Aristotle (384-322 BCE) who was considered the standard by which any claims were measured. Posidonius' calculations resulted in a smaller circumference for the earth but, because they had become more popular than Eratosthenes', were the ones used in the bestselling work Almagest of the astronomer Ptolemy (100-170 CE) which would continue to exert considerable influence up through the European Renaissance. Although Eratosthenes' calculations were still in use, Posidonius' system was considered valid by virtue of its inclusion in Ptolemy's work, and it was Posidonius' calculations that Christopher Columbus (1451-1506) used to convince his patrons to sponsor him as he was able to show them how short a trip across the Atlantic Ocean would be. Eratosthenes' system was more accurate, however, and was used by many European ship captains and cartographers effectively throughout the Age of Exploration. In the present day, Eratosthenes' calculations are understood as being closer to the actual circumference of the earth than either Posidonius or Aristotle and he is recognized as one of the greatest intellectuals of antiquity. Subscribe to topic Related Content Books Cite This Work License Bibliography Auden, W. H. The Portable Greek Reader . Penguin Classics, 2006. Empiricus, Sextus & Bury, R. G. Outlines of Pyrrhonism . Prometheus Books, 2010. Heath, T.L. Greek Astronomy . Cambridge University Press, 2014. Livingstone, R.W. The Legacy of Greece. Oxford University Press, 2014. Strabo & Roller, D. W. The Geography of Strabo. Cambridge University Press, 2014. Waterfield, R. The First Philosophers: The Presocratics and the Sophists. Oxford University Press, 2009. About the Author Translations We want people all over the world to learn about history. Help us and translate this definition into another language! Questions & Answers Who was eratosthenes, what is eratosthenes famous for, why is eratosthenes called the father of geography, who first discovered the size of the earth, what was eratosthenes' primary influence, related content. Greek Mathematics Greek Astronomy Jesuit Influence on Post-medieval Chinese Astronomy Astronomy in the Scientific Revolution Hipparchus of Nicea Eratosthenes' Calculation of the Earth's Circumference Free for the world, supported by you. World History Encyclopedia is a non-profit organization. For only $5 per month you can become a member and support our mission to engage people with cultural heritage and to improve history education worldwide. Recommended Books External Links Cite this work. Mark, J. J. (2022, March 03). Eratosthenes . World History Encyclopedia . Retrieved from https://www.worldhistory.org/Eratosthenes/ Chicago Style Mark, Joshua J.. " Eratosthenes ." World History Encyclopedia . Last modified March 03, 2022. https://www.worldhistory.org/Eratosthenes/. Mark, Joshua J.. " Eratosthenes ." World History Encyclopedia . World History Encyclopedia, 03 Mar 2022. Web. 19 Aug 2024. License & Copyright Submitted by Joshua J. Mark , published on 03 March 2022. The copyright holder has published this content under the following license: Creative Commons Attribution-NonCommercial-ShareAlike . This license lets others remix, tweak, and build upon this content non-commercially, as long as they credit the author and license their new creations under the identical terms. When republishing on the web a hyperlink back to the original content source URL must be included. Please note that content linked from this page may have different licensing terms. +30.210.8176795 [email protected] ERATOSTHENES ANNOUNCEMENT 2023 ANNOUNCEMENT 2022 Main Event 2022 ANNOUNCEMENT 2021 MAIN EVENT 2021 LESSON PLANS WINNER MARCH 2024 PHOTO CONTEST 2024 WINNER MARCH 2023 WINNER MARCH 2022 WINNER SEPTEMBER 2019 WINNER MARCH 2019 WINNER SEPTEMBER 2018 WINNER MARCH 2018 WINNER MARCH 2017 WINNER SEPTEMBER 2016 WINNER MARCH 2016 WINNER MARCH 2015 ERASTOSTHENES You are here. WHO Eratosthenes WAS  Eratosthenes  was a talented mathematician and geographer as well as an astronomer. He made several other important contributions to science. Eratosthenes devised a system of latitude and longitude, and a calendar that included leap years. He invented the armillary sphere, a mechanical device used by early astronomers to demonstrate and predict the apparent motions of the stars in the sky. He also compiled a star catalog that included 675 stars. His measurement of the circumference of Earth was highly respected in his day, and set the standard for many years thereafter. He may have also measured the distances from Earth to both the Moon and to the Sun, but the historical accounts of both deeds are, unfortunately, rather cryptic. A crater on Earth's Moon is named after Eratosthenes. HOW HE DID IT In 240 B.C., the Greek astronomer Eratosthenes made the first good measurement of the size of Earth. By noting the angles of shadows in two cities on the Summer Solstice, and by performing the right calculations using his knowledge of geometry and the distance between the cities, Eratosthenes was able to make a remarkably accurate calculation of the circumference of Earth. Eratosthenes lived in the city of Alexandria, near the mouth of the Nile River by the Mediterranean coast, in northern Egypt. He knew that on a certain day each year, the Summer Solstice, in the town of Syene in southern Egypt, there was no shadow at the bottom of a well. He realized that this meant the Sun was directly overhead in Syene at noon on that day each year. Eratosthenes knew that the Sun was never directly overhead, even on the Summer Solstice, in his home city of Alexandria, which is further north than Syene. He realized that he could determine how far away from directly overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object. He measured the length of the shadow of a tall tower in Alexandria, and used simple geometry to calculate the angle between the shadow and the vertical tower. This angle turned out to be about 7.2 degrees. Next, Eratosthenes used a bit more geometry to reason that the shadow's angle would be the same as the angle between Alexandria and Syene as measured from the Earth's center. Conveniently, 7.2 degrees is 1/50th of a full circle (50 x 7.2° = 360°). Eratosthenes understood that if he could determine the distance between Alexandria and Syene, he would merely have to multiply that distance by 50 to find the circumference of Earth! Eratosthenes had the distance between the two cities measured. His records show that the distance was found to be 5,000 stadia. The stadion or stade (plural = stadia) was a common distance unit of the time. Unfortunately, there was not a universal, standard length for the stadion; so we don't know exactly which version of the stadion Eratosthenes used, and therefore are not exactly sure how accurate his solution was. He may have been correct to within less than 1% (if used the Greek stadion that was approx. 155 meters), a remarkable accomplishment! Or, if it was actually a different stadion (if used the Italian attic stadion that was approx. 185 meters) that he used, he may have been off by about 16%. The actual polar circumference of Earth is just a bit over 40 thousand km (about 24,860 miles). Eratosthenes's only tools were sticks, eyes, feet and brains; plus a zest for experiment. With those tools he correctly deduced the circumference of the Earth, to high precision, with an error of only a few percent. That's pretty good figuring for 2200 years ago. - Carl Sagan -  More on Eratosthenes Experiment How did he take the measurement? nike jordan six rings | SBD , Meek Mill adidas Ultra Boost Triple Black , adidas Superstar Foundation "Core Black/White" ORGANISED BY Ellinogermaniki Agogi Research & Development Department Dimitriou Panagea Street GR 15351 Pallini The Eratosthenes Experiment is endorsed by the European project   GEOACADEMY .  GET IN TOUCH Dr. Angelos Lazoudis Phone: +30.210.8176795 Email: [email protected] © Copyright 2023 by Ellinogermaniki Agogi. All Rights Reserved. 160 IMAGES Eratosthenes Year 9 & Eratosthenes Eratosthenes Experiment Eratosthenes' experiment, illustration Eratosthenes' experiment Eratosthenes' experiment. Diagram showing the measurements and COMMENTS READ: Eratosthenes of Cyrene (article) Learn how the ancient Greek scholar Eratosthenes used geometry, trigonometry, and a well in Egypt to estimate the size of the Earth. Explore his achievements in geography, astronomy, and mathematics. Eratosthenes Experiment 2024 Join the global event on March 21, 2024 to calculate the circumference of the Earth using simple tools and eLearning. See the results, photos and winners of the previous Eratosthenes Experiment and the photo contest. The Eratosthenes experiment: calculating the Earth's circumference Learn how to measure the Earth's circumference like Eratosthenes did 2300 years ago using a stick's shadow and simple calculations. Find out the geometry, trigonometry, and geography behind this ancient feat of scientific thinking. This measurement is more than 2,200 years old, and its accuracy is His little experiment demonstrated that the surface of the earth was curved like a sphere. ... Eratosthenes knew that the distance between Syene and Alexandria was 7.2 degrees along the surface of ... EAAE Eratosthenes' experiment was one of the most important experiments in antiquity and his estimate of the earth's size was accepted for hundreds of years afterwards. It was, in fact, the most accurate estimate until Man was able to go to Space. Details. Last Updated: 14 June 2019. Measure Earth's Circumference with a Shadow Observations and results In 200 B.C. Eratosthenes estimated Earth's circumference at about 46,250 kilometers (28,735 miles). Today we know our planet's circumference is roughly 40,000 kilometers ... PDF Eratosthenes' Determination of Earth's Circumference Learn how Eratosthenes calculated the circumference of Earth using the angle of the sun at two locations. Find out the equipment, methods, and examples for this ancient experiment. Eratosthenes Calculates the Circumference of the Earth Eratosthenes reasoned that the ratio of the angular difference in the shadows to the number of degrees in a circle (360°) must equal the ratio of the distance to the circumference of the Earth. The resulting estimate, about 25,000 miles (40,234 km), is astonishingly accurate. In making his calculations Eratosthenes measured distance in stadia ... Astronomy 101 Specials: Eratosthenes and the Size of the Earth So Eratosthenes made this measurement and found that the value for angle ``A'' is 7.2 degrees. He also knew that the actual distance between Alexandria and Syene was 5040 stades (1 stade = about 160 m) because somebody had measured it out by foot. Well 7.2 degrees is only 7.2/360ths of the way around the globe (since all the way around is 360 ... Eratosthenes Eratosthenes (born c. 276 bce, Cyrene, Libya—died c. 194 bce, Alexandria, Egypt) was a Greek scientific writer, astronomer, and poet, who made the first measurement of the size of Earth for which any details are known.. At Syene (now Aswān), some 800 km (500 miles) southeast of Alexandria in Egypt, the Sun's rays fall vertically at noon at the summer solstice. How Did Eratosthene Calculate The Circumference Of Earth In 240 BC? Eratosthene calculated the circumference of Earth by measuring the length of a stick's shadow in Alexandria and the distance between Alexandria and Syrene on foot. He then took the inverse tangent of the ratio between the shadow's length and the stick's length to find the angle of inclination of the Sun. He calculated the total ... Eratosthenes: Measuring the Impossible Learn how the Greek mathematician Eratosthenes calculated the circumference of the Earth using only a stick, a well and trigonometry. Discover his ingenious method and the accuracy of his result, despite the limitations of his time. Eratosthenes: The Measurement of the Earth's Circumference Repeat Eratosthenes' Experiment. A simplified explanation of Eratosthenes' Experiment Eratosthenes and the Circumference of the Earth from Rogue Robot on Vimeo. Eratosthenes measured, at his local noon in Alexandria, the angle of elevation of the sun on the summer solstice (21 June). Eratosthenes used the local noon and no other time of the day ... Discovering the size of the Earth: The Eratosthenes experiment Eratosthenes' ingenious experiment involved observing the sun's angle at noon on the summer solstice in two different cities - Syene and Alexandria - which were located at the same longitude. He noticed that at noon on the summer solstice, the sun was directly overhead of a well in Syene, without casting any shadows, while in Alexandria ... Eratosthenes Eratosthenes of Cyrene (/ ɛr ə ˈ t ɒ s θ ə n iː z /; Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC - c. 195/194 BC) was an Ancient Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist.He was a man of learning, becoming the chief librarian at the Library of Alexandria.His work is comparable to what is now known as the study of geography, and ... How Eratosthenes calculated the Earth's circumference In the mid-20th century we began launching satellites into space that would help us determine the exact circumference of the Earth: 40,030 km. But over 2000 ... How an Ancient Greek Calculated the Earth's Circumference He could then use simple proportions to find the Earth's circumference—7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers. And just like that, an ancient Greek calculated precisely the circumference of our entire planet with just a stick and his brain over two thousand years ago. Eratosthenes accomplished many ... Eratosthenes Measures Earth Modern scholars disagree about the length of the stadium used by Eratosthenes. Values between 500 and about 600 feet have been suggested, putting Eratosthenes' calculated circumference between about 24,000 miles and about 29,000 miles. The Earth is now known to measure about 24,900 miles around the equator, slightly less around the poles. Circumference of Earth (video) Eratosthenes found a way, using none of the modern tools that we have, to measure the circumference of the Earth. And in this video, we're going to see how he did this. So the heart of Eratosthenes's measurement is a simple geometry problem. So consider the circle shown here, which has points A and B. Eratosthenes Eratosthenes (l. c. 276-195 BCE) was a Greek astronomer, geographer, mathematician, and poet best known for being the first to calculate the circumference of the earth and its axial tilt. He is also recognized for his mathematical innovation, the Sieve of Eratosthenes, which identified prime numbers, and his position as head of the Library at Alexandria. Eratosthenes A versatile scholar, Eratosthenes of Cyrene lived approximately 275-195 BC. He was the first to estimate accurately the diameter of the earth. For several decades, he served as the director of the famous library in Alexandria. He was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. ERASTOSTHENES Eratosthenes was a talented mathematician and geographer as well as an astronomer. He made several other important contributions to science. Eratosthenes devised a system of latitude and longitude, and a calendar that included leap years. He invented the armillary sphere, a mechanical device used by early astronomers to demonstrate and predict ... essay homework paper phd project resume review study thesis