What is Eratosthenes formula?

You can figure out the earth’s circumference using a geometric formula that’s over 2,000 years old! Eratosthenes divided 360° by 7.2° and got 50, which told him that the distance between Alexandria and Syene (500 miles) was 1/50 of the total distance around the Earth.

What mathematical principle did Eratosthenes use to conclude that the two cities were 7.2 apart?

If we extend the lines of two vertical objects they will meet at the center of the Earth and the angle formed by these two lines will be also equal to the angle α. Eratosthenes determined that the two cities were α = 7.2 degrees apart.

What is Eratosthenes theory?

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.

How Eratosthenes measured the circumference of the Earth?

Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 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.

Is Eratosthenes method of determining the circumference of the Earth logical and reasonable?

Eratosthenes also calculated the distance from the Earth to the Moon and to the Sun, but with less accuracy. Yet his most lasting achievement was his remarkably accurate calculation of the Earth’s circumference (the distance around a circle or sphere).

Who measured Earth’s circumference?

The Greek philosopher Aristotle (384-322 B.C.) is credited as the first person to try and calculate the size of the Earth by determining its circumference (the length around the equator) He estimated this distance to be 400,000 stades (a stadia is a Greek measurement equaling about 600 feet).