Yes, I know that in 1882 Lindemann proved that π (3.141) is transcendental, but nobody has ever proved that π = 3.141. The way the value is currenlty calculated is by using a method of integration, and as you can see here, I believe at best it is a very close approximation.
Therefore, this site is dedicated to the search for a mathematical proof using any method not based on integration.
Pi and the squared circle
In the following interactive diagram, please use the following versions of 4/π and comment below, which one you think is the correct value.
a) 1.2732395447351626861510701069801 (calculator Pi)
b) 1.2712753453503583545403454617905 (rootwo Pi)
c) 1.2720196495140689642524224617375 (golden Pi)