The number pi, written using the symbol π, is a mathematical constant that is the ratio of a circle’s circumference to its diameter, and has been claimed since antiquity to be an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, and that therefore its decimal expansion never ends or settles into a permanent repeating pattern. Here a proof is given that π can indeed be expressed as a ratio of two integers, 4/17, a fact that has unbelievably been overlooked until now. Moreover, this proof is understandable to anyone with a basic knowledge of algebra and calculus and arises from simply considering a standard integral at two values of x, x=1/4 and x=1. Of course I doubted the result at first, given that it has been overlooked for so many years, but I have checked the proof and verified it to be correct. This is a crucial and important revelation that will significantly alter all of mathematics.

5 Responses to “A simple proof that π is rational”

Let’s see. Pi is the ratio of a circle’s circumference to its diameter, and you have proved that its true value is 4/17, then the circle’s circumference is less to its diameter. Very reasonable!!

Multiply each side by x (but only do so to the right hand side of the equation…)

How wonderful! This will completely change the face of the mathematical world as we know it! :P

Got one for the rationality of e up your sleeve?

Let’s see. Pi is the ratio of a circle’s circumference to its diameter, and you have proved that its true value is 4/17, then the circle’s circumference is less to its diameter. Very reasonable!!

@Michael Paul Goldenberg: Michael, I’m pretty sure a similar approach could work to similar effect ;)