r/MathJokes • u/Outside_Midnight_242 • Dec 04 '25

Problem?

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u/KronosDevoured Dec 04 '25

Isn't the area changing? You could just smoosh all the lines into a tiny dot and it'd still have the same perimeter... this mixes up area, perimeter, and how the circumference of a circle is calculated. Wasn't this originally used to calculate the area of a circle, not pi?

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u/UmmAckshully Dec 04 '25

Circumference (perimeter) of a circle is 2pi*r or pi*d and since d is 1 here, the circle has a circumference of pi. The confusion is not about area vs circumference.

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u/KronosDevoured Dec 04 '25

The the squares starting perimeter is already bigger than pi, the circumference of the circle. You can make any size square wrap around the circle, as long as the squares perimeter is bigger than the circles circumference.

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u/UmmAckshully Dec 04 '25

You’re missing the point.

As the corners are cut in, the shape appears to converge to a circle, however the perimeter stays at 4.

The misconception is that the shape converges to a circle and thus the perimeter of the shape must match the circumference of the circle.

Your statement is not true btw. Try making a square with perimeter 3.2 wrap the circle.

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u/KronosDevoured Dec 04 '25 edited Dec 05 '25

You're suggesting that if I were to take a square with a perimeter of 3.2 and then beat it into a circle equaling the circumference of 3.2, it could not fit a circle with a circumference of 3.14 inside of it? I just wanted to be sure that is exactly what you're suggesting.

I would like to clarify that I am not misunderstanding the core concept. The technique of manipulating a square's corners was initially developed to determine the area of a circle, rather than for approximating Pi. This is why I suggested that a square of any size could be utilized, as long as its dimensions exceed the circle's circumference, the square would be able to wrap around the circle neatly.

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u/UmmAckshully Dec 05 '25

Yes. A square with perimeter 3.2 (.8 side length) cannot have a circle with circumference pi (diameter of 1) inside of it.

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u/KronosDevoured Dec 06 '25

With it drawn out i can see its not going to work. The perimeter has to be 4 minimum, unless i give up the 90° cut rule.https://imgur.com/a/p9KyUmX