Who Found the Circumference of the Earth? Eratosthenes and His Groundbreaking Calculation
The person credited with accurately calculating the circumference of the Earth is Eratosthenes of Cyrene, a Greek polymath living in the 3rd century BC. His ingenious method, relying on simple geometry and astute observation, yielded a result remarkably close to the actual circumference.
Eratosthenes: The Man Behind the Measurement
Eratosthenes wasn’t just a mathematician; he was a librarian, geographer, astronomer, and poet, serving as the chief librarian at the Library of Alexandria, one of the ancient world’s greatest centers of learning. His diverse interests and sharp intellect enabled him to make significant contributions across various fields, but his calculation of the Earth’s circumference remains his most celebrated achievement. This feat demonstrates the power of observation, reasoning, and basic mathematics in understanding the world around us.
The Observations That Sparked an Idea
The story begins with Eratosthenes learning about a peculiar phenomenon in the city of Syene (modern-day Aswan, Egypt). It was said that on the summer solstice, the sun shone directly down a deep well, indicating that it was at the zenith – directly overhead. Eratosthenes, knowing that this didn’t happen in Alexandria, located further north, suspected the Earth was curved. If the Earth were flat, the sun’s rays would hit both cities at the same angle.
The Power of Angles and Distances
Eratosthenes reasoned that the difference in the angles of the sun’s rays between Syene and Alexandria could be used to calculate the Earth’s circumference. He measured the angle of the shadow cast by a vertical object (likely a gnomon) in Alexandria on the summer solstice. This angle was found to be approximately 7.2 degrees, or about 1/50th of a circle (360 degrees). Assuming the distance between Alexandria and Syene was approximately 5,000 stadia (the exact length of a stadium is debated but estimated around 157.5 meters), he multiplied this distance by 50 to arrive at his estimated circumference.
The Result: A Triumph of Ancient Science
His calculation resulted in an estimated circumference of 250,000 stadia. Converting this to modern units is challenging due to the uncertainty surrounding the length of the stadium. However, even using the most conservative estimates, Eratosthenes’ calculation was remarkably accurate, coming within a few percentage points of the actual circumference of the Earth (approximately 40,075 kilometers). This incredible feat, achieved with limited tools and resources, cemented Eratosthenes’ place in history as a pioneer of scientific measurement and geographical understanding.
Frequently Asked Questions (FAQs)
Here are some frequently asked questions about Eratosthenes and his groundbreaking calculation:
FAQ 1: What tools did Eratosthenes use to measure the Earth’s circumference?
Eratosthenes’ primary tools were a gnomon (a vertical rod used to measure shadows), his knowledge of geometry, and the reported distance between Alexandria and Syene. While the exact methods used to measure that distance remain debated, historical accounts suggest it was done by carefully paced walking or perhaps by surveying techniques of the time. The key element was accurate angle measurement using the gnomon and the knowledge of the angular difference representing a fraction of the entire circle.
FAQ 2: How accurate was Eratosthenes’ calculation of the Earth’s circumference?
Eratosthenes’ calculation is estimated to be remarkably accurate, falling within 2% to 20% of the actual value, depending on the assumed length of the stadium. While the uncertainty surrounding the ancient unit of measurement (the stadium) makes pinpointing the exact accuracy challenging, his method was fundamentally sound, and his result was a testament to his ingenuity.
FAQ 3: What assumptions did Eratosthenes make in his calculation?
Eratosthenes made several crucial assumptions. He assumed:
- That the Earth was a perfect sphere.
- That Alexandria and Syene lay on the same meridian (line of longitude).
- That the sun was so far away that its rays were practically parallel when they reached the Earth.
While these assumptions aren’t perfectly accurate, they were reasonable approximations that allowed him to perform his calculation.
FAQ 4: Why was Eratosthenes’ calculation so important?
Eratosthenes’ calculation was incredibly important because it provided the first relatively accurate estimate of the Earth’s size. This was a monumental achievement that challenged previous estimations and significantly advanced geographical knowledge. It also demonstrated the power of scientific reasoning and observation.
FAQ 5: Did other ancient civilizations attempt to measure the Earth’s circumference?
Yes, other civilizations made attempts, but Eratosthenes’ method was the most successful and widely adopted. Earlier attempts were often based on less rigorous methods and yielded less accurate results. Some ancient scholars speculated on the Earth’s size, but Eratosthenes provided the first calculation based on empirical observation and geometric principles.
FAQ 6: What is the “stadium” and how long was it?
The stadium was an ancient unit of length used in Greece and other parts of the ancient world. Its exact length is debated among historians, with estimates ranging from 157 meters to 209 meters. This uncertainty makes it difficult to convert Eratosthenes’ result into modern units with absolute precision.
FAQ 7: How did Eratosthenes use geometry in his calculation?
Eratosthenes used the principles of Euclidean geometry, specifically the properties of parallel lines and transversals. He understood that the angle of the sun’s rays at Alexandria was the same as the angle at the Earth’s center subtended by the arc between Alexandria and Syene. Knowing the distance between the cities and the angle, he could then calculate the total circumference.
FAQ 8: Was Eratosthenes’ calculation accepted by everyone in his time?
While Eratosthenes’ calculation was influential, it wasn’t universally accepted immediately. Some scholars questioned his assumptions or proposed alternative measurements. However, over time, his result gained acceptance and became a cornerstone of ancient geographical knowledge.
FAQ 9: How did Eratosthenes’ work influence later scientific discoveries?
Eratosthenes’ work paved the way for more accurate mapmaking and navigation. His calculation of the Earth’s circumference provided a crucial foundation for understanding the Earth’s size and shape, which was essential for developing accurate maps and navigating the seas. It also served as an inspiration for future generations of scientists and mathematicians.
FAQ 10: What is a gnomon and why was it important for Eratosthenes’ calculation?
A gnomon is a vertical rod or pillar used to measure the angle of the sun by observing the length and direction of its shadow. It was crucial for Eratosthenes’ calculation because it allowed him to precisely measure the angle of the sun’s rays at Alexandria on the summer solstice, providing the key angular measurement needed for his calculation.
FAQ 11: What were the limitations of Eratosthenes’ method?
While ingenious, Eratosthenes’ method had limitations. The accuracy of his result was dependent on the accuracy of the distance measurement between Alexandria and Syene and the accuracy of his angle measurement. Furthermore, his assumption of a perfectly spherical Earth and the alignment of Alexandria and Syene on the same meridian introduced potential sources of error.
FAQ 12: Can Eratosthenes’ experiment be replicated today?
Yes, Eratosthenes’ experiment can be replicated today using basic materials like a stick, a measuring tape, and a protractor. By measuring the shadow cast by the stick at different locations at the same time and knowing the distance between those locations, students can calculate an estimate of the Earth’s circumference, demonstrating the power of his simple yet elegant method.
Eratosthenes’ calculation of the Earth’s circumference remains a testament to human ingenuity and the enduring power of scientific inquiry. His work stands as a reminder that profound discoveries can be made with simple tools and a curious mind.