How Does Leibniz Formula for Pi/4 - A Pi Day Visualization/Dissection Work?

Pi/4 is like a puzzle made from shapes that get smaller and smaller, and when you add them all up, you find Pi.

Imagine you have a square pizza cut into four equal pieces, each piece is a right triangle. Now picture this: if you keep cutting those triangles in half again and again, you're making tiny little triangles that look like slices of a circle. This is how Leibniz’s formula for Pi/4 works, it adds up the areas of all these tiny triangles to get closer to Pi.

Each time you cut the triangle in half, you're adding a new piece that's smaller than before. It’s like stacking paper, each sheet is thin, but together they make a big pile. The more triangles you add, the closer you get to the full size of the circle.

Think about how we measure things: if you know the area of one triangle, and you have many similar ones, you can figure out how much of the whole pizza they cover. That’s exactly what Leibniz did, he used math patterns to find Pi/4 by adding up all those tiny triangles, just like counting slices of a pizza.