114 questions linked to/from The staircase paradox, or why $\pi\ne4$
8k views

### Two paradoxes: $\pi = 2$ and $\sqrt 2 = 2$ [duplicate]

Possible Duplicate: Is value of $\pi = 4$? Can anyone explain how to properly resolve two paradoxes in this YouTube video by James Tanton?
2k views

### Problem with the Pythagorean theorem [duplicate]

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 ...
379 views

### Why is this proof for $1 = 2$ incorrect? [duplicate]

Think of a triangle such that the length of all sides are $1$. Note that the sum of the two black sides is always $2$. So, the sum of the black sides in the last triangle is $2$. Note that the bottom ...
613 views

### Constructing a circle from a square [duplicate]

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 ...
949 views

### Pythagorean "Paradox" (right-angled triangle). [duplicate]

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 ...
345 views

### Is $\pi = 4$ really? [duplicate]

Can anyone explain what's wrong with this?
241 views

### How does $a^2 + b^2 = c^2$ work with ‘steps’? [duplicate]

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 ...