(side of the inner square)/ diagonal of the inner square, and π had to lie somewhere in between these two numbers. (side of the outer square)/ side of the outer square and 4. It is interesting how Archimedes in his papers used the term “diameter.” So, what is the diameter of a square, is it the diagonal or the edge, turns out it is both! Archimedes considered the effective lengths (the edge of the outer square and the diagonal of the inner square) for each square, A circle can be thought of as a polygon with infinite sides, which was exactly the thought process used by Archimedes to calculate π!Īrchimedes first thought of calculating π by fitting a square inside and outside a circle so they are all touching each other and then dividing the perimeter of the squares by the diameter.
Think about this, a square is a little like a circle, but when a side is added to form a pentagon, it comes closer to resembling one, and when another side is added it gets more closer, and so on. The ancient mathematicians were struck by the problem of calculating the length of a curved surface, though they could have used easier methods like using a string to measure the length and then find the value by comparing it with a linear scale, they stuck to the method of exhaustion. The way π was initially calculated by a method known as the method of exhaustion, you will soon enough know why it was called the method of “exhaustion.” The Babylonians found the value of π to be around 3.125, which happens to be accurate to 1%! and given these calculations date back to when iron was first used by the human civilization, this is astonishingly accurate!
The evidence of which was found in the Ishango bone, and maybe even before that! While the knowledge of counting spread and mathematics as a whole developed, both the ancient Babylonians and the Egyptians attempted to find the value of π. Ishango bone | Source: Counting, the very basis of mathematics dates back to 20,000 BC.