Einstein’s First Proof

The proof relies on two insights. The first is that a right triangle can be decomposed into two smaller copies of itself . That’s a peculiarity of right triangles. If you try instead, for example, to decompose an equilateral triangle into two smaller equilateral triangles, you’ll find that you can’t. So Einstein’s proof reveals why the Pythagorean theorem applies only to right triangles: they’re the only kind made up of smaller copies of themselves. The second insight is about additivity.

The same thing works for any right triangle of any shape. It doesn’t have to be isosceles. The triangle always occupies a certain fraction,, of the square on its hypotenuse, and that fraction stays the same no matter how big or small they both are.

Throughout his career, Einstein would continue to deploy symmetry arguments like a scalpel, getting to the hidden heart of things. He opened his revolutionary 1905 paper on the special theory of relativity by noting an asymmetry in the existing theories of electricity and magnetism: “It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena.

Great article! If you're into Einstein, you might be interested in my novel about zapping the most intelligent human beings from the past into the present and getting any unsolved questions about the world answered. :)

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