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A simple proof that π is rational

The number $\pi$, the ratio of a circle’s circumference to its diameter, long thought to be an irrational number and commonly written as 3.141, is found in many areas of mathematics and science and has been studied throughout the ages.

The ubiquitous nature of $\pi$ makes it all the more surprising that the world wakes up this Monday to a startling new result: $\pi$ is rational. This new result makes a mockery of much of modern mathematics, including recent results and ongoing debates reported on this site. The proof is a picture of elegance and can be understood by anyone with knowledge of basic algebra and calculus.

The author of this new result is Peter Rowlett, maths educator and sometime podcast reneger from Nottingham, England. Rowlett posted the result on his blog this morning, presumably in order to make the result public as soon as possible ahead of publication in a peer-reviewed journal, which will surely follow in time. Rowlett says he now plans to submit his new result for a PhD in the Summer.

More information is available in the original paper: A simple proof that $\pi$ is rational.

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

  1. blasjdedhj

    Hello, I think I may have spotted a mistake in your proof:

    “8x^2 = 8(x + x + . . . + x).
    Multiply each side by x:
    8x^2 = 8x(x + x + . . . + x).”

    You seemed to have only mulitplied the RHS by x in the 2nd line. So when you did your differentiation, you should have ended up with: 24x^2=16x^2, concluding that x=0.

    I may have overlooked something though.


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