Triangle Geometrical Paradox

[Steve Prevette]

In Reply to Parent Post by keego

Thanks all, it's mathematically sound. But that still doesn't explain why I can cut these shapes out of graph paper (and using a straight edge to draw the hypotenuse) and duplicate the 'hole'.

Because it is NOT a hypotenuse. Neither big shape is a triangle. The top shape (which is 4 sided) is not the same shape as the lower shape (which is 4 sided).

[keego]

I believe you Steve, and the math. But I suggest you perform this exercise with graph paper, a steel rule, and scissors. Then you'll see what I'm talking about.

[Steve Prevette]

And if you take the two triangles you have cut out, and overlay one on top of the other, you will see that the hypotenuses have two different slopes.

[smryan]

In paper cutouts you would have to be superman to see the difference, true enough. It's challenging enough in pixels.

[Steve Prevette]

http://en.wikipedia.org/wiki/Missing_square_puzzle

[keego]

In Reply to Parent Post by Steve Prevette

And if you take the two triangles you have cut out, and overlay one on top of the other, you will see that the hypotenuses have two different slopes.

How is that possible? I used a steel rule to define the slope(s). They have to be the same.

[Steve Prevette]

In Reply to Parent Post by keego

How is that possible? I used a steel rule to define the slope(s). They have to be the same.

OK, my last response on this. Count the squares. The slopes are different on the two small triangles. Look at the wikipedia article and many many other internet writeups on this and other "dissection" puzzles that end up looking the same, but are subty different.