Linked Questions
108 questions linked to/from The staircase paradox, or why $\pi\ne4$
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
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. ...