Transcending Irrationality by Squaring the Circle

As a keen follower of I Fucking Love Science, I have noticed the growing interest in the pi day why I want to make my own contribution to the celebration. To what extent pi day really is today of course depends on which date format you prefer, but disregarding that, π nevertheless is an interesting concept.

π is a mathematical constant, defined as the ratio of a circle's circumference to its diameter, commonly approximated as 3.1415926. But it also has other characteristics worth mentioning such as that it is an irrational number, having decimals that never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed, although no proof of this has been discovered yet which of course means that a large number of mathematicians are still trying to do so. Also, π is a transcendental number which implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.

Now, I don't understand why anyone would want to square a circle unless you consider the idiom "square peg in a round hole" for example occuring in the chick-flick movie "The Holiday", sadly shown every Christmas on Swedish television.

To me "squaring the circle" is more interesting as a metaphor than as a mathematical activity. Apparently it has come to mean "to try to do the impossible". Been there, done that. However, since it has been proven by Ferdinand von Lindemann in 1882 that squaring the circle is impossible, it should be used with caution since it is really difficult to prove that something is impossible and not just hard. Of course, you can always do what mathematicians often do: cheat. Or, in their language, do an approximation.

From Cambridge UK 2015

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