"A good sketch is better than a long speech", as Napoleon once said. This is true in mathematics too, although figures, drawings, and diagrams were long banished from "serious" books—even geometry texts. Today, we again recognize the visual side of a proof and the intuition a diagram can foster: with a single glance, the light dawns and we exclaim: "Of course!" So even if "showing is not proving", drawings and diagrams may not build an argument, but they can at least help us find a path towards one. Here we revisit these proofs without words, which help us visualize situations that may not appear geometric, or properties that might otherwise go unnoticed.
Figures, but no words
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When we think of "figures", we naturally think of "geometry"—and no field has proved more fertile ground for proofs without words. A Chinese manuscript dating back to 200 BCE already provides an example, making the celebrated Pythagorean theorem self-evident (see Tangente 172, 2016).
