Sunday, May 29, 2011

Missing square puzzle

From Wikipedia
The missing square puzzle is an optical illusion used in mathematicsclasses to help students reason about geometrical figures. It depicts two arrangements of shapes, each of which apparently forms a 13×5 right-angled triangle, but one of which has a 1×1 hole in it.

 Is it possible? Okay, Here's your hint...

Can you calculate the slope of the line that goes through the diagonal of the whole piece of graph paper? It's change in Y over change in X, or -13/5. Okay, what about the slope of the diagonal line that is part of the red triangle? Hmmm...that would be -8/3.

WAIT A MINUTE! Those aren't the same number! -13/5 does not equal -8/3! You know what that means, don't you? The dimensions of the red triangle aren't REALLY 8x3! And guess what! The dimensions of the blue triangle are not really 5x2!

I'll leave it to you to figure out the rest...

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