FE Meme
Tilt the Protractor: Globe Math Breaks?
#12: Globe-model Eratosthenes math fails because tilting a protractor or angle meter on a slope gives the wrong reading, so shadow-angle proofs of Earth's size are invalid.
The Meme
Two-panel meme: top shows a protractor/angle meter on a tilted surface with "WRONG READING"; bottom shows Eratosthenes' stick-and-shadow diagram labelled "GLOBE MODEL CALCULATIONS."
Why It Spreads
Everyone has placed a protractor on a crooked desk and gotten a nonsense angle. The meme pastes that everyday mistake onto Eratosthenes' stick-and-shadow diagram, making a 2,300-year-old proof look like amateur hour without explaining what was actually measured between two cities.
What It Gets Wrong
The two-panel meme shows a protractor giving a wrong reading on a tilted surface, then labels Eratosthenes stick-and-shadow math as broken globe calculations, but Eratosthenes compared noon shadow angles in Alexandria and Syene roughly 800 km apart on the same meridian using vertical gnomons. The angle difference θ between those two cities feeds C ≈ (360°/θ) × D and yields a circumference near 40000 km, which fits modern GPS-coordinate replications. Tilting one classroom tool on a local hillside is inconsistent with the inter-city measurement the method actually uses. TestTheGlobe's A Local Sun Explains Day and Night and TestTheGlobe's Eratosthenes Earth Size Calculator walk through the observations and predictions this image skips.
The Debunk
Simultaneous noon shadows hundreds of kilometres apart predict an Earth circumference near 40000 km via C ≈ (360°/θ) × D; modern replications with GPS coordinates fit that observation. A tilted protractor on one slope is inconsistent with Eratosthenes' two-city angle difference method. Use TestTheGlobe's Eratosthenes Earth Size Calculator to compare the meme's claim with a measurable prediction.
- TestTheGlobe's A Local Sun Explains Day and Night: the measured input is the difference between two noon shadow angles ~800 km apart, not a single instrument on a tilted surface.
- TestTheGlobe's Eratosthenes Earth Size Calculator: Syene saw the Sun overhead at noon on the solstice; Alexandria did not; that offset θ is the latitude separation Eratosthenes used in C ≈ (360°/θ) × D.
- TestTheGlobe's Eratosthenes Earth Size Calculator lets you enter two latitudes and shadow data to reproduce the ~40000 km result.
- TestTheGlobe's Two-Stick Shadow Experiment walks through the same geometry with modern coordinates, independent of local ground tilt on one protractor demo.