Is Pi more than just a ratio for circles? Is there a easy way to understand the universality of Pi?
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If you measure from the center of a circle the distance to the edge will always be the same.
Since the distance will always be the same (definition of a circle)… If you make a triangle from the middle of a circle to a place around the circle the long end will always also be a consistent length.
Those triangles are the basis of trigonometry and geometry.
Triangles are really easy to work with. You can measure their sides and you can easily measure their surface area. Imagine measuring the area or volume of a box. Easy. Triangle, nearly as easy. Now imagine measuring the area of a jelly bean! That’s super hard. However, if we can convert a jellybean paper cutout to just a bunch of triangles… Easy again!
Even pi can be calculated that way. We break a circle into lots of pizza slices and then we know the area of each pizza slice triangle. When we add together a whole lot of really thin slices of pizzas we can approximate pi.
But once we have a sufficiently accurate measurement of pi, we can use that number in all kinds of triangles and angles.
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