π (pi) is the ratio of a circle's circumference to its diameter. This is true for any circle, so to calculate π, let's pick a circle with a radius of 1, which is called a unit circle. Since the radius is 1, the diameter is 2:

Calculate π by finding the circumference. Unfortunately, it's hard to measure the circumference of a circle accurately. But it's easy to measure straight lines, so put a hexagon inside of the circle, which is called an inscribed polygon. Measure the circumference of the hexagon to get an approximation of π. To do that, divide the hexagon into equilateral triangles:

Since the radius of the circle is 1, each side of the hexagon is 1. So the circumference of the hexagon is 1 × 6, which is 6. Plug that in to get an approximation of π:

To get a better approximation of π, double the sides of the hexagon, and measure the circumference of the 12-sided polygon. To do that, draw lines from the center of the circle to each of the vertices:

There are now many right triangles. Using the Pythagorean theorem and algebra, you can derive an equation for the length of a side of the 12-sided polygon, labeled side₂. The equation is based on the length of a side of the hexagon, labeled side₁:

Work out the equations shown in blue to get the value of side₂. Multiply that by 12 to get the circumference of the 12-sided polygon. Plug that in to get a better approximation of π. Continue doubling the sides and working out the same equations to get better and better approximations of π.