Lunar Terminator Paradox

Dima Kogan investigates the "lunar terminator paradox," an optical illusion where the moon's bright limb appears to point away from the sun after sunset. He explains the effect with simple geometry and a small program: when the sun is effectively behind the observer (as for a full moon on the horizon), the same part of the lunar surface stays illuminated as the moon rises, but the observer moves to a position "below" that illuminated hemisphere. That change in viewing angle reveals dark crescent on the bottom edge of the disk, making the bright region look like it's pointing up. The effect grows stronger for fuller phases and vanishes for exact half-moons.

He produced two visual scans to demonstrate specifics: one follows a 3/4 moon from horizon to zenith and shows increasing dark area at the bottom, and another fixes the moon at 60° elevation while sweeping the sun's azimuth to show how a lit crescent on the bottom can persist and how the disk transitions through half-phase at 90°. He also reports that conversational AIs (Claude, Gemini) failed to reason this out, and notes that the text is public domain while the code is LGPL.