Eratosthenes erected a pole in Alexandria, and on the summer solstice he observed that it cast a shadow, proving that the Sun was not directly overhead but slightly south. Recognizing the curvature of the Earth and knowing the distance between the two cities enabled Eratosthenes to calculate the planet’s circumference.
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.
How would you measure the circumference of the Earth?
The circumference of the Earth can be calculated using the formula, Circumference = 2 πR or π D, where R is the radius of Earth and D is the diameter. By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found.
How did Eratosthenes measure the circumference of the Earth quizlet?
How did Eratosthenes estimate the size of Earth? They measured the angle of the Sun above the horizon at midday in two places with different latitude and used the angle to estimate the circumference of Earth.
What method did Eratosthenes use?
Eratosthenes method was very simple; he measured the length of a shadow from a vertical stick of a known height in two cities on the same day. The ratio between the north-south distance between the two cities and the angles measured gave a ratio which allowed Eratosthenes to calculate the size of the Earth.
What was Eratosthenes method?
Quote from video: That man was Eratosthenes a Greek mathematician in the head of the Library of Alexandria. Eratosthenes had heard that in Syene a city to the south of Alexandria. No vertical shadows were cast at noon
How was the first mathematician measured the circumference of the Earth?
How Eratosthenes calculated the Earth’s circumference
How is Eratosthenes calculated?
Eratosthenes combined this measurement with the distance between Syene and Alexandria, about 4,400 stades. If we plug these numbers into the above equation, we get: (360°÷ 7.12°) which equals 50; and 50 x 4,400 equals 220,000 stades, or about 25,000 miles.
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