# Linked Questions

92 questions linked to/from The staircase paradox, or why $\pi\ne4$
4answers
7k 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?
2answers
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 ...
2answers
272 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 ...
1answer
300 views

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

Can anyone explain what's wrong with this?
1answer
200 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 ...
1answer
238 views

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 ($\frac{\pi}{... 1answer 288 views ### Length of diagonal compared to the limit of lengths of stair-shaped curves converging to it [duplicate] I see this post and I am stunned. I think this is fallacious but I can't figure where is the fallacy? If you know the fallacy. Please post a answer. 0answers 183 views ### contradicting PI=4 fallacy. [duplicate] Possible Duplicate: Is value of$\pi = 4$? I know that you can take area out of a square without changing it's perimeter. Now, here's this problem: Draw a circle with dia = 1; Draw a square ... 1answer 119 views ### This proof is wrong. How? (See image in link below) [duplicate] Came across this on the internet. I have some ideas regarding this but I wanted to know more such reasonings. 0answers 142 views ### Pythagorean “Paradox” (right-angled triangle). [duplicate] Consider an isosceles right-angled triangle as shown in the figure (top left). The length of its hypotenuse is$c$. The figure distinguishes both legs of the triangle, however, from now on let's ... 1answer 101 views ### What is wrong with this reasoning when calculating circle perimeter? [duplicate] Looking at the following image, which was posted on the internet: Could someone tell me what is wrong? It seems true for the first 4 small images. But, when it comes to infinitesimal length, ... 2answers 47 views ### Approximating a circle vs a diagonal. [duplicate] Situation 1: A regular$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$-gon approaches the ... 0answers 55 views ### Approaching the diagonal is Funky [duplicate] Here is something really funky that popped up in my head as I was thinking about walking across my room, which is a rectangle. Let's assume that it has side lengths of a and b. Now, If I walk from one ... 0answers 52 views ### Getting a wrong value of$\pi$[duplicate] I read this question somewhere Let a square of length 1 unit and a circle is inscribed in it such that it touches the sides of square. Now cut small portion(outside the circle) of square from each ... 1answer 45 views ### Diagonal ladder length [duplicate] Let$ 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 ...

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