# Tagged Questions

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How is it possible to prove a paradox? Also, can someone explain the Banach-Tarski paradox in layman's terms (for someone up to calc 3 and ODEs knowledge)?
259 views

### Elementary proof that there is no paradoxical decomposition using triangular pieces

I am teaching a geometry course and I am trying to understand two definitions in the textbook ("Geometry with Geometry Explorer" by Michael Hvidsten.) Definition: The area of a rectangle is its base ...
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### What is the problem? [duplicate]

Where has the one block gone in lower image,after we rearrange the triangles? (Found it on G+ as a post.)
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### 8 x 8 = 13 x 5 ???

I'm sure some (if not most) have seen this by now and since I'm fairly new to real deep mathematical explorations I'm stumped as to why this would be true. For class I was asked to cut out an 8" x ...
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?
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### Fractal walking: well defined case or not?

Please consider the following recursive diagram: diagram Each triangle is connected at the midpoint of a side to the corner of an inner triangle which is 1/4 times the size. The total line length of ...