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Plant a stick. That is the whole machine.
The sun draws a shadow. Taller stick, longer shadow — but the lean of the light stays put.
You do not need a lab. You need a stick in the dirt. The stick, the shadow, and the sunbeam make a skinny triangle. The only number that matters is how much the light leans — the little corner at the top of the stick. Stretch the stick and the shadow stretches with it. The lean does not care.
Drag the sun. Eratosthenes did not need the length of the shadow. He needed the lean.
In your life
A flagpole at noon. A lamppost. You, standing in a playground. The same machine is still running, every sunny day, for free.