#2**+11 **

Thanks anon,

That is an approximation of pi.

If you roll a wheel one complete rotation then it will travel exactly $${\mathtt{\pi}}$$ times the diameter of the circle in distance.

pi is an irrational number which means that it cannot be expessed exactly in digits.

It is approximately 3.14158

[I give credit to flflvm97 for first using this Gif on the forum. Thanks fl :) ]

Melody
Dec 14, 2014

#3**+8 **

It can be shown that the curve traced out by a point on this wheel is known as a cycloid. It's arc length through one rotation can be found by using Calculus and is equal to 8r, where "r" is the radius of the wheel....!!! Also, the area under one arc is just .... 3*pi*r^2......

Here's a reference....if you're interested.....http://www.mathalino.com/reviewer/cycloid-equation-length-arc-area

CPhill
Dec 14, 2014