Astronomers

Eratosthenes

Eratosthenes: The Man Who Measured the Earth

Eratosthenes of Cyrene, a Greek polymath living from 276 to 196 BC, stands as a towering figure in the history of science. While known for his contributions to various fields, his most remarkable achievement was a remarkably accurate measurement of the Earth's circumference – a feat that predated the modern scientific era by centuries.

Born in Cyrene, a Greek colony in modern Libya, Eratosthenes studied in Athens before becoming the Librarian at the famed Library of Alexandria. This prestigious position provided him access to a vast repository of knowledge, which he utilized to delve into diverse disciplines including geography, mathematics, astronomy, and philosophy.

Eratosthenes' genius shone through in his approach to measuring the Earth's circumference. He employed a simple yet ingenious method, leveraging the knowledge that the Sun's rays hit different parts of the Earth at varying angles.

He observed that on the summer solstice, the sun cast no shadow in Syene (modern Aswan) in Egypt, indicating it was directly overhead. Simultaneously, he measured the angle of the sun's rays in Alexandria, finding it to be about 7 degrees.

Eratosthenes cleverly reasoned that the difference in the angle of the sun's rays was proportional to the distance between Syene and Alexandria. He calculated the distance between the two cities to be about 5,000 stadia (an ancient unit of measurement). Then, using basic geometry and the assumption that the Earth is a sphere, he extrapolated the full circumference, reaching an astonishingly accurate figure of around 40,000 kilometers.

This measurement, though not perfect, was incredibly close to the actual circumference of the Earth, which is roughly 40,075 kilometers. His achievement cemented his place in history as one of the pioneers of scientific inquiry, demonstrating the power of observation, logic, and simple mathematics to unravel the mysteries of the universe.

Eratosthenes' legacy extends beyond his groundbreaking measurement. He is also known for developing a system of prime number identification, known as the "Sieve of Eratosthenes," a method still used today. His contributions to geography were equally significant, with the creation of the first accurate map of the known world.

Eratosthenes' life serves as a reminder of the boundless potential of human ingenuity. His remarkable accomplishments in a variety of fields stand as a testament to the power of curiosity, critical thinking, and the pursuit of knowledge. His pioneering work laid the foundation for future generations of scientists, pushing the boundaries of human understanding and shaping the course of scientific discovery.


Test Your Knowledge

Quiz: Eratosthenes: The Man Who Measured the Earth

Instructions: Choose the best answer for each question.

1. What was Eratosthenes' most famous accomplishment?

a) Developing the Sieve of Eratosthenes. b) Creating the first accurate map of the known world. c) Measuring the circumference of the Earth. d) Writing the first book about astronomy.

Answer

c) Measuring the circumference of the Earth.

2. What method did Eratosthenes use to measure the Earth's circumference?

a) He used a telescope to observe the stars. b) He calculated the Earth's diameter using the moon's shadow. c) He observed the angle of the sun's rays at different locations. d) He measured the distance traveled by a ship around the Earth.

Answer

c) He observed the angle of the sun's rays at different locations.

3. Where did Eratosthenes observe the sun casting no shadow on the summer solstice?

a) Alexandria b) Athens c) Cyrene d) Syene

Answer

d) Syene

4. What was Eratosthenes' measurement of the Earth's circumference approximately?

a) 20,000 kilometers b) 30,000 kilometers c) 40,000 kilometers d) 50,000 kilometers

Answer

c) 40,000 kilometers

5. Which of the following fields did Eratosthenes NOT contribute to?

a) Geography b) Mathematics c) Physics d) Astronomy

Answer

c) Physics

Exercise: Eratosthenes' Method

Instructions: Imagine you are Eratosthenes trying to measure the Earth's circumference. You have two cities, City A and City B, located on the same meridian.

  • On the summer solstice, you observe that the sun is directly overhead in City A (casting no shadow).
  • You measure the angle of the sun's rays in City B to be 5 degrees.
  • You know the distance between City A and City B is 3,000 kilometers.

Using this information and Eratosthenes' method, calculate the approximate circumference of the Earth.

Exercice Correction

Here's how to solve the exercise:

1. **Angle Proportion:** The 5-degree difference in the sun's angle represents a fraction of the Earth's full circle (360 degrees). This fraction is 5/360.

2. **Distance Proportion:** The 3,000 kilometer distance between the cities represents the same fraction (5/360) of the Earth's circumference.

3. **Calculate Circumference:** To find the full circumference, set up a proportion: 5/360 = 3,000 / Circumference

4. **Solve for Circumference:** Cross-multiply and solve for the unknown: 5 * Circumference = 360 * 3,000 Circumference = (360 * 3,000) / 5 Circumference = 216,000 kilometers

Therefore, based on these measurements, the approximate circumference of the Earth is 216,000 kilometers. While not completely accurate, it demonstrates the principle behind Eratosthenes' method.


Books

  • A History of Greek Science by George Sarton (A comprehensive overview of Greek science, including a detailed chapter on Eratosthenes)
  • The Measure of the Earth: The Wonderful Story of Eratosthenes and the First Measurement of the Circumference of the World by E.H. Gombrich (A captivating and accessible account of Eratosthenes' life and achievement)
  • Eratosthenes of Cyrene: A Biography by T.L. Heath (A scholarly biography delving into Eratosthenes' contributions to various fields)
  • The Seven Wonders of the Ancient World by David Keys (Contains a chapter on Eratosthenes and his measurement of the Earth)
  • The History of Mathematics by Carl B. Boyer (A classic history of mathematics with a section on Eratosthenes and his work in geometry and number theory)

Articles

  • "Eratosthenes of Cyrene: The Man Who Measured the Earth" by Michael J. Crowe in The American Mathematical Monthly (A detailed analysis of Eratosthenes' method for measuring the Earth)
  • "The Sieve of Eratosthenes" by David M. Bressoud in The American Mathematical Monthly (An explanation of Eratosthenes' sieve method for prime number identification)
  • "Eratosthenes and the Measurement of the Earth" by James Evans in The British Journal for the History of Science (A scholarly exploration of Eratosthenes' scientific methodology)

Online Resources


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