Linked Questions

21
votes
4answers
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?
11
votes
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 ...
0
votes
2answers
384 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 ...
1
vote
1answer
329 views

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

Can anyone explain what's wrong with this?
2
votes
1answer
219 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 ...
3
votes
0answers
573 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 ...
2
votes
1answer
406 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.
-1
votes
1answer
245 views

How to find the area. Linked with another question. [duplicate]

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}{...
1
vote
0answers
206 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 ...
0
votes
1answer
142 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.
-2
votes
1answer
129 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, ...
0
votes
1answer
90 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 ...
0
votes
1answer
38 views

Why are the shortest distances in Euclidean geometry not taxicab? [duplicate]

I am of course well aware that distances in Euclidean geometry are calculated from the Pythagorean theorem. This is more of a conceptual question. My question may also be formulated as follows: If we ...
0
votes
2answers
54 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 ...
0
votes
1answer
45 views

When does the distance traveled in vertical and horizontal lines become the hypotenuse? [duplicate]

I am looking for a formal proof for the following problem: You travel from point A to point B on a right triangle only along its legs. For a 3 4 5 right triangle you would travel a distance of seven. ...

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