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Possible Duplicate: Is value of $\pi = 4$? Can anyone explain how to properly resolve two paradoxes in this YouTube video by James Tanton?

The Pythagorean theorem has already been proved and it is a basic fact of math. It always works, and there are proofs of it. But I have found a problem. Say you want to get from point ...

I have seen a [picture like this] several times: featuring a "troll proof" that $\pi=4$. Obviously the construction does not yield a circle, starting from a square, but how to rigorously and ...

Can anyone explain what's wrong with this?

We all know that $a^2+b^2=c^2$ in a right-angled triangle, and therefore, that $c<a+b$, so that walking along the red line would be shorter than using the two black lines to get from top left to ...

Possible Duplicate: Is value of $\pi = 4$? In this question we discussed why the fake proof is wrong. But, what about the area? The process converges to the same area of the circle ($\frac{\pi}{...

I see this post and I am stunned. I think this is fallacious but I can't figure where is the fallacy? If you know the fallacy. Please post a answer.

Possible Duplicate: Is value of $\pi = 4$? I know that you can take area out of a square without changing it's perimeter. Now, here's this problem: Draw a circle with dia = 1; Draw a square ...

Came across this on the internet. I have some ideas regarding this but I wanted to know more such reasonings.

Consider an isosceles right-angled triangle as shown in the figure (top left). The length of its hypotenuse is $c$. The figure distinguishes both legs of the triangle, however, from now on let's ...

Looking at the following image, which was posted on the internet: Could someone tell me what is wrong? It seems true for the first 4 small images. But, when it comes to infinitesimal length, ...

Situation 1: A regular $n$-gon is inscribed in a circle. As $n$ increases without bound, the area of the $n$-gon approaches the area of the circle and the perimeter of the $n$-gon approaches the ...

Here is something really funky that popped up in my head as I was thinking about walking across my room, which is a rectangle. Let's assume that it has side lengths of a and b. Now, If I walk from one ...

I read this question somewhere Let a square of length 1 unit and a circle is inscribed in it such that it touches the sides of square. Now cut small portion(outside the circle) of square from each ...

Let $ ABCD $ be a square with side length $ a $. Let $ s $ be a staircase from $ A $ to $ C $ with total length $ l $ and number of steps $ n $. It consists of perpendicularly alternating lines of ...