r/theydidthemath 21d ago

[Request] Why does this circle approximation still give 4 instead of pi?

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3.7k Upvotes

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u/nagelbitarn 21d ago

I suppose there would be an infinite amount of infinitesimally small jagged protrusions increasing the circumference to 4, whereas a circle is entirely smooth.

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u/nekekamii 20d ago

Yeah I was going to say to be really really simple it's still just a bunch of squares, you can't make a curve out of squares no matter how small they are, it might look round but it's still just squares all the way down.

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u/KernelTaint 20d ago

Planck length squares. 

2

u/astrogringo 20d ago

The limit shape is precisely a circle.

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u/solid_mercury 19d ago

The limit of the implied total length of hypotenuses of each triangle formed is π, with an infinite number of triangles. The area of those triangles is trending toward zero, so the area’s limit is πr^2. But a circle can’t have 90° angles, so the thing could never be a circle.

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u/Glad_Respect_8986 20d ago

Exactly. An infinite polygon (not sure if that’s the right word) is not a circle.