3k 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?
454 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 ...
144 views

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

Can anyone explain what's wrong with this?
182 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 ...
65 views

### How does $a² + b² = c²$ work with 'steps'? [duplicate]

We all know that $a²+b²=c²$ 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 ...
101 views

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 ...
15k views

### Best Fake Proofs? (A M.SE April Fools Day collection) [closed]

In honor of April Fools Day 2013, I'd like this question to collect the best, most convincing fake proofs of impossibilities you have seen. I've posted one as an answer below. I'm also thinking of a ...
13k views

### Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
17k views

### Is $.999999999… = 1$?

I'm told by smart people that $0.999999999... = 1$ and I believe them, but is there a proof that explains why this is?
110k views

### How many sides does a circle have?

My son is in 2nd grade. His math teacher gave the class a quiz, and one question was this: If a triangle has 3 sides, and a rectangle has 4 sides, how many sides does a circle have? My first ...
5k views

### How to convince a layman that the $\pi = 4$ proof is wrong?

The infamous "$\pi = 4$" proof was already discussed here: Is value of $\pi$ = 4 ? And I have read all the answers, yet I think that they will not be of much help to me if I try to explain this ...
4k views

### Paradox: increasing sequence that goes to $0$?

It is $10$ o'clock, and I have a box. Inside the box is a ball marked $1$. At $10$:$30$, I will remove the ball marked $1$, and add two balls, labeled $2$ and $3$. At $10$:$45$, I will remove the ...
### Is $\pi$ more transcendent than $e$?
I’ve often wondered about this, and I conjecture the affirmative, based mainly on that it is so much easier to prove the transcendence of $e$ than that of $\pi$. I would be surprised if, just as ...