who was the first person to calcalate the circumference of the earth and coined the word "Geography"

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The first person credited with calculating the circumference of the Earth and coining the word "Geography" is Eratosthenes, a Greek mathematician, astronomer, and geographer who lived around the 3rd century BCE.

To understand how Eratosthenes calculated the Earth's circumference, you can follow these steps:

1. Eratosthenes noticed that during the noon of the summer solstice (June 21st), the Sun was positioned directly overhead in the city of Syene (known today as Aswan), located in southern Egypt.

2. Eratosthenes knew that at the same time in Alexandria, a city located to the north of Syene, the Sun formed an angle with the vertical. By measuring this angle, he sought to calculate the circumference of the Earth.

3. He estimated the distance between Alexandria and Syene to be about 800 kilometers (approximately 500 miles). This was done by measuring the distance traveled by camels over a period of time.

4. On the day of a summer solstice at noon, Eratosthenes used a vertical measuring tool such as a staff or a gnomon at Alexandria. He recorded the angle of the Sun's rays by measuring the length of the shadow cast by the tool.

5. Using the information gathered, Eratosthenes calculated the angle formed by the rays of the Sun between the vertical at Alexandria and the rays reaching the ground directly overhead in Syene.

6. Assuming that the angle formed at Alexandria represented 1/50th of a full circle (360 degrees), Eratosthenes used simple proportion to estimate the Earth's circumference. Thus, he multiplied the measured distance between Alexandria and Syene by 50 to determine the Earth's total circumference.

It's worth noting that Eratosthenes' calculation was remarkably accurate for his time, resulting in an estimate of approximately 39,375 kilometers (24,662 miles) for the Earth's circumference. This accounts for less than a 2% error compared to the actual measurements taken with modern techniques.

Additionally, Eratosthenes is known for his contributions to various fields, including geography, astronomy, mathematics, and poetry. His works laid the foundation for future advancements in these disciplines.