Does Pi Equal 2?? (Spoiler: no)





In this short, we show a thought experiment that arises by doubling the number of semicircles drawn in a semicircle but halving their radii. The process produces an infinite collection of smaller and smaller chains of more and more semicircles that always have combined circumference length equal to pi. If we think about the limiting process, it seems like maybe this technique shows that pi = 2. But Pi can definitely be shown to be greater than 3 – so where does this argument fail?

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Here is a related false proof that shows root 2 is equal to 2:

This false argument was suggested to me by Jeff Stuart as a nice alternative to the more classic Pi = 4 argument.

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35 Replies to “Does Pi Equal 2?? (Spoiler: no)”

this is literally the same as the pi = 4 "proof" 😢 tired of seeing it. just bc when you fold something up and it appears smaller doesn't mean it's actually smaller. it's just dense

What perplexes me is that, in this example, half the distance of pi is roughly 1.57, (pi/2=1.57), so the total length of pi is nearly 1.5x the length of the diameter.
Idk, Circumferences and hypotenuses always surprise me.

Ooh this is the exact same fallacy as the the problem where you can take the distance around a square and repeatedly add more and more 90° turns to make it look like a right triangle, but keep the same perimeter. Basically they never actually fundamentally change what shape they are, therefore they do not adobt the properties of the shape that they look like

Well if we cut 2 into infinte number of x where x is radius of one circle we get x + x + x +…. = 2
So x times infinity is equal to 2 so x is infinitely close to 0. We get pi x + pi x + …. = pi from our first observance so infinity times pi times x = pi so x times infinity equals one which would contradict our previous findings. Even if those two infinites arent the same (bcs yes they arent all the same) then even simple logic is sufficient. Going infinitely close to 0 with radius doesnt mean you will actually get that so at no point you will prove pi equals 2 because that would mean you reached infinity which is impossible in standard numbers

this is kinda stupid , u can solve that without just making curves .
Since when radius equals the angle of curve .
If so , this give pie infinite values .
If u set the radius to be infinity then pie equals infinity and there u know that theres no more maths .
And we are all over again

They never flatten out actually. They just slowly get smaller, than anything we have to measure things. Still 2D space, still 2D figure, just in smaller pieces.

well even the slightest difference between lengths of curve and line becomes big as the number of semicircles in the sequence tends to Infinity as the difference between the two lengths tends to Zero

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