How Did the Ancient Greeks Calculate Pi Without Calculators?

The ancient Greeks figured out Pi by wrapping strings around circles and measuring them with rulers, finding that a circle’s wide part is always about three times its tall part.

Imagine you have a round pizza pan. If you take a piece of string and lay it straight across the middle from one side to the other, that is the diameter. Now, if you wrap that same string all the way around the edge of the pan, it will be longer. The Greeks discovered that no matter how big your circle is, the round distance (the circumference) is always a little more than three times the straight line across.

Since they did not have calculators or computers, they used shapes with many flat sides to guess the curve. They drew a shape inside a circle and another outside it, like a triangle fitting snugly in a bowl while another triangle sits on top of it. By counting the length of all those straight lines for the inner shape and comparing them to the outer shape, they got a very tight estimate for Pi. It is like trying to measure a wiggly worm by holding it down with many tiny fingers to see how much space it takes up.

This clever trick was called the Method of Exhaustion. They kept adding more sides to their shapes, turning triangles into hexagons and then into shapes with twenty-four sides. Each time they added a side, their measurement became more precise because the flat edges hugged the curve tighter. It is similar to how you might trace a round coin by rolling it along a ruler; the more times you roll it carefully, the better your guess becomes. They did not need high tech tools, just patience, straight lines, and really good eyes!