How can circumference of circle (`C = 2 pi r`) be derived?
This question, believe it or not, is likely going to be the easiest to answer on this website. The reason? The equation is derived from the definition of `pi`!
`pi` is defined as the ratio of a circle's circumference to its diameter, which is twice the radius. It was found during the days of the Greeks that this ratio was constant, no matter what the size of the circle. Thus, they gave it a special symbol: `pi`. Put into the form of an equation:
Notice that "triple" equal sign. This symbol simply means "is defined as." In other words, it can be replaced by a normal equal sign, but this particular symbol just has the extra point of saying "this is what we mean whenever we use the symbol `pi`."
To get the circumference, we simply multiply both sides by `2r`:
`2pi r = C`
There you have it! Your circumference can be easily found by that equation, which is simply the result of how we defined `pi` back in ancient times. I hope that helps!