WOLFRAM|DEMONSTRATIONS PROJECT

Dissection Fallacy

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step
the problem
solution
another view
proof
adjust/shift the figures
64 ≠ 65
Look at the two rectangles. The colored pieces are the same, so the rectangles should have the same area. But multiplying the base by the height for each shows the areas are different. What's wrong?
A well-known example of a dissection fallacy. An apparent paradox arises when you rearrange the pieces of a dissected square into a 'rectangle'. Find the solution examining the figures carefully!