10
votes
3answers
248 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 ...
0
votes
0answers
51 views

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.)
1
vote
0answers
153 views

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 ...
13
votes
4answers
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?
0
votes
1answer
86 views

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 ...