A highly imaginative visual proof of an Arithm…

A highly imaginative visual proof of an Arithmetic Mean-Geometric Mean Inequality (abbreviated AM-GM).

The volume of any pyramid is 1/3(b*h). Given three right pyramids, made from cubes with bases of x, y, and z (yellow, red, and blue respectively), the total volume is

To account for the right hand side of the inequality, observe that the dotted lines outline an empty cuboid region with volume xyz. You can see that the pyramids are too large to fit the region*, satisfying the inequality.

*Unless x=y=z, in which case the regions are of equal volume.

Mathematics is beautiful. <3

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