# The process of calculating the earths circumference by eratosthenes

There was a tall tower in Alexandria. Eratosthenes will always be remembered for the calculation of the Earth's circumference circa BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene now Aswan, Egypt.

When the chief librarian of the famous Library of Alexandria died in BCE, Eratosthenes was appointed to the prominent position around the age of SIT, You want to measure the length of the meter stick's shadow-from the base of the meter stick to the tip of the shadow-when the sun is at its highest point in the sky.

Now it's easy to calculate the Earth circumference by using the following formula: Hipparchus second century B. Eratosthenes lived in the city of Alexandria, near the mouth of the Nile River by the Mediterranean coast, in northern Egypt. First, calculate your local noon because it may be quite different from You want to be set up and ready to measure the shadow length about ten minutes before this time so that you don't miss it.

Compute the circumference of the earth using the distance and angle measurements you have. The actual radius of the earth is 6, Experiment Requirements Before I begin, understand that this is a fun experiment and we are going to do it with everyday objects that includes the internet.

If Eratosthenes used the Olympic stadion of Today, we know that thet equatorial circumference of Earth is 40, In the midth century we began launching satellites into space that would help us determine the exact circumference of the Earth: Read more Astronomer Astronomers think big!

However, the date is September 25 missed the equinox by two days and the sun is overhead somewhere at 0. The Earth is Spherical He measured the angle made by the pole and a line joining the tip of the shadow and the top of the pole see Figure 1 and found the angle to be about 7o.

In other words the distance line has to cut the Tropic of Cancer at a right angle. From the representation of the orbit of Venus, it is clear that there are two places where the Sun-Venus-Earth angle is 90 degrees. Wherever Eratosthenes found in his sources data such as distances in stades, similarities in fauna, flora, climate, or astronomical phenomena, lengths of the longest days, etc.Once this Earth-Venus distance is known, the distance between Earth and the Sun can be calculated.

As you have indicated, once the distance between Earth and Sun is known, one can calculate all the other parameters. We know that the Sun, as seen from Earth, has an angular diameter of about degrees.

Calculation Eratosthenes used the angular difference in latitude of two points on the same meridian and the corresponding linear distance between the points to determine the distance on the surface of the Earth per degree of latitude.

The crux of the argument centers on the unusual form of the runes used on the rune stone, including the infamous “Hooked X®,” more accurately a variant of the rune for “A” in which an extra line is attached as a branch on one of the staves of the X-shaped rune.

Editor's Note: This article was the winning article in the competition for best history of mathematics article by a student, sponsored by the History of Mathematics SIGMAA of the Mathematical Association of America. In the third century BCE, the brilliant librarian Eratosthenes of Cyrene ( BCE) devised an ingenious method by which to measure the circumference of the Earth.

By measuring the shape (and inventing contour lines in the process!) it is possible to calculate the volume.

From rock sampling, you can then calculate the mass of the mountain. Looking at pendulum deflection, you can calculate the ratio of the mass of the Earth to the mass of Schiehallion. Recognizing the curvature of the Earth and knowing the distance between the two cities enabled Eratosthenes to calculate the planet’s circumference. Eratosthenes could measure the angle of the Sun’s rays off the vertical by dividing the length of the leg opposite the angle (the length of the shadow) by the leg adjacent to the angle (the height of the pole).

The process of calculating the earths circumference by eratosthenes
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