WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Dissection Fallacy

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!

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.

I understand and wish to continue anyway »