**Pythagoras theorem.**

On November 26, 1949, Albert Einstein published an essay in the Saturday Review of Literature in which he described two pivotal moments in his childhood. The first involved a compass that his father showed him when he was four or five. The second involved his early exposure to Euclidean plane geometry. He was impressed by the idea that a mathematical assertion could “be proved with such certainty that any doubt appeared to be out of the question”.

Steven Strogatz discusses a breathtakingly simple proof of the Pythagorean theorem whose provenance is traced to Einstein as a child. "Though we cannot be sure the following proof is Einstein’s, anyone who knows his work will recognize the lion by his claw."

The proof is at <A HREF="https://www.newyorker.com/tech/annals-of-technology/einsteins-first-proof-pythagorean-theorem">Einstein's first proof.</A>

<sub>The proof relies on the insight 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.</sub>