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[Kernel Sohcahtoa]

Come on guys, it took until page 6 for someone to reply properly? When he set us up so perfectly? I'm ashamed in you all.

Welcome to the forum polymath! I love math, haven't studied beyond intro calculus so far though. What's your view on using approximations in calculations (ex. pi = 3)?

It depends on what you are calculating and why. For example, if the irrationality of the number is important, using pi=3 would be a very idea. If, instead, you want to get an order of magnitude estimate for some physical process, it would be useful.

The point is that pi is NOT the same as 3 or 22/7 or 355/113. It is an irrational number. It is even a transcendental number (not the root of any polynomial with integer coefficients). There are cases where this is an important aspect of the number pi.

But, for example, we do not know whether pi+e is irrational or not. Most mathematicians suspect it is, but nobody has found a proof. There is no way to tell this by an approximation.

Have you attempted to prove this? Has anyone come close?