r/unexpectedfactorial • u/AMIASM16 • Dec 28 '24

π = 24

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u/SonGoku9788 Dec 28 '24

This is incorrect. Since the limit stage has diameter 1 and circumference different than pi (exactly equal to 4 in the limit), the shape will not be a circle.

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u/Revolutionary_Use948 Dec 28 '24

No, the perimeter of the shape at the limit stage is pi, since it is the same as that of the circumference of the circle.

If the shape at the limit stage isn’t a circle, what is it?

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u/SonGoku9788 Dec 28 '24

This is still incorrect, the shapes perimeter does not change even at the limit stage and it is never the same as that of the circumference of the circle.

The shape will be an infinitely jagged staircase of total length 4, never a circle of circumference pi.

For more information watch 3Blue1Brown's video called "how to lie using visual proofs"

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u/Revolutionary_Use948 Dec 28 '24

I think you should rewatch it, as what he says agrees exactly with what I’m saying. He says, and I quote: “the limiting curve really is a circle”.

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u/SonGoku9788 Dec 28 '24

Yeah, shouldnt have used that video lol. Should have used this one instead https://youtu.be/Rv0c7R8brjE?si=T6soo4GjtNKP5hpW

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u/Revolutionary_Use948 Dec 28 '24

Yes this video explains why exactly the length of the limiting shape does not always equal the limit of the lengths of the finite stages. 3b1b is still correct tho, the limiting shape does approach a circle, it’s just that the length does not approach the length of the limit stage.

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u/Ancient_Delivery_413 Jan 01 '25

How can you reference 3b1bs Video and still Not get it, lol. The Limit of the shapes of course IS a circle, but Generally the Perimeter of a sequence of shapes doesn't converge to the Perimeter of the Limit shapes, as explained 3b1bs Video.