>>13483047As Wildberger says, Mathematics has a problem with lacking explicit definitions, so lets be precise. Pi is the ratio of a circle's circumference to its diameter. not a constant that is found at the top of a computer program that is precise to what ever floating point precision the computer is giving you. It is a relationship.
The prime definition of a real number, is "a continuous quantity that can represent a distance along a line". Paradoxically, the definition is extended to irrational numbers, whose infinite precision can never be expressed as a distance along a line by drawing it in sand, or crafting a piece of wood at that length. It can only be conceptualised in the mind.
To highlight this doublethink, I elucidate the quadrature of the circle with keplers triangle. Setting the diameter of the circle to phi, an irrational number, and the length of the square to 1. (explicitly found here
http://measuringpisquaringphi.com/pi-math-proof/) what we see is that, according to this proof, Pi is not what were taught!
Whether you not agree this is the true value of pi and we've had it wrong all along is beside the point. This represents a case of attempting to perform geometry on a shape that doesn't technically exist in nature, nothing real about it.
