1. Observation: Eratosthenes noticed that on the summer solstice, the sun shone directly down a well in Syene (modern-day Aswan, Egypt). This meant the sun was directly overhead at noon. At the same time, in Alexandria, located further north, the sun cast a shadow at a specific angle.
2. Measurement: He measured the angle of the shadow cast by an obelisk in Alexandria. This angle was approximately 7 degrees.
3. Geometry: Eratosthenes realized that the angle of the shadow was directly related to the angle between the two cities on the Earth's surface. Since the sun's rays are essentially parallel, the angle of the shadow is equivalent to the angle between the two cities' positions on the Earth's circumference.
4. Calculations: Eratosthenes assumed the distance between Syene and Alexandria was approximately 5,000 stadia (an ancient unit of measurement). Using his knowledge of geometry, he realized that if the 7-degree angle represented 1/50th of a full circle (360 degrees), then the distance between Syene and Alexandria was 1/50th of the Earth's circumference.
5. Circumference: He calculated the Earth's circumference to be 250,000 stadia. While the exact conversion to modern units is debated, this equates to roughly 40,000 kilometers (24,855 miles), which is remarkably close to the actual circumference of the Earth (40,075 kilometers or 24,901 miles).
Key points:
* Eratosthenes' method relied on the assumption that the Earth was a sphere.
* The accuracy of his measurement depended on the accuracy of the distance between Syene and Alexandria and the angle of the shadow.
* Despite these limitations, Eratosthenes' calculation was an impressive feat of scientific reasoning and observation. It was the first known attempt to calculate the Earth's circumference and paved the way for future advancements in geography and astronomy.
