I understand the mathematical definition of Pi, but why does it end up being used in so many formulas and applications in math, engineering, physics, etc? What does it unlock?
Edit: I understand Pi is the ratio of circumference to diameter. But why is that fact make it important and useful. For example it shows up in the equation for standard normal distribution. What does Pi have to do with a normal distribution. That’s just one example.
In: 3
It is, essentially, the conversion factor between polar and rectilinear (Cartesian) systems, the constant that is needed to convert an arcuate (circles and friends) shape into a linear output. An awful lot of math revolves around a choice of coordinates where each axis is perpendicular to the others. Circles don’t really fit perpendicular coordinates, so to deal with the effects of a circle in a rectilinear system, we have to do a conversion. Pi is the constant required to make that conversion.
Describing a circle in x-y-z space is hard, but it is also hard to describe a rectangle in polar (magnitude, direction) coordinates. Whichever system you choose, there will be shapes that are hard to describe without a means to convert, and pi is part of that means, the constant that is used to make the conversion.
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