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no historical likeness exists

c. 624 – c. 546 BCEMiletus, ancient Ionia (modern-day Turkey)

Thales of Miletus

Two shapes are similar when one is a scaled copy of the other, and from that you can measure the unreachable.

A short story

An ancient Greek thinker from Miletus on the Aegean coast, traditionally regarded as the first named mathematician in the Greek tradition. He is most famous for an elegant trick: by comparing the length of a person's shadow to their height, he calculated the height of the Great Pyramid of Giza without ever climbing it. The sun's rays are (very nearly) parallel, so any two upright things on flat ground cast similar shadows, and the ratio of height to shadow is the same for the stick and the pyramid. Rearrange, and the unreachable becomes measurable.

In their own words

He set up a stick where the pyramid's shadow ended, and showed that the two heights were in the same ratio as the two shadows.

Paraphrased: from Plutarch's Convivium Septem Sapientium, c. 100 CE, recounting Thales' pyramid-shadow measurement.

The lab their idea turned into

Shadow Lab

Two shapes are similar when one is a scaled copy of the other, and from that, you can measure the unreachable.

Open Shadow Lab