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Circumference of a circle
By Iain Shelvington and Jenny Human on February 20, 1998:

Who first worked out how to measure the perimeter of a circle?

And how is it done?


From Iain Shelvington and Jenny Human Year 5

By Anonymous:

Dear Iain and Jenny,

It is often difficult to be sure who first worked out a mathematical method. Often the person whose name is remembered was using, building on and recording earlier work.

Ahmes (about 1700 BC) recorded calculations of the area of a circle in The Rhind Papyrus. He used an octagon (and not a regular one) to get answers close to the true value.

Much more accurate results were found by Archimedes (about 260 BC) by drawing polygons. He drew circumscribed regular polygons, with their sides just touching the circle. The perimeters of the polygons get closer and closer to the circumference of the circle as you take polygons with more and more sides.

These polygons are outside the circle and the answers are TOO BIG, but how much too big? Archimedes answered this question by drawing inscribed regular polygons (inside the circle) with their vertices on the circle. Again this method gives better and better answers as you take polygons with more sides but this time the answers are TOO SMALL.

In this way Archimedes was able to get as close to the real answers as anyone wanted.

You can try it for yourselves. If you do, please let us know how you get on. Have fun!

NRICH

By Sujata Krishna on March ??, 1998:

The early measurements of the circumference of a circle are particularly interesting when you think about measuring the size of the Earth. An Egyptian called Eratosthenes in 230 BC in Alexandria developed a method to measure the Earth using the shadow of a stick.

Eratosthenes was born in 273 BC in Cyrene on the north coast of Africa, educated in Athens, and came to Egypt in his thirties. He was a contemporary of Archimedes. Archimedes used to send Eratosthenes mathematical problems to solve, and then sent the solutions along later, in case he'd got stuck - a bit like NRICH does for you! Eratosthenes was a brilliant geographer, and a fine astronomer, and used a combination of his skills to measure the size of the Earth. You can see how he calculated the circumference of the Earth at this link.