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← All topicsGeometry Puzzles
16 articles · 3 checkpoints · 9 deeper reads · 4 reference notes
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Break a stick at two random points into three pieces, what's the chance they form a triangle? The puzzle rewards translating a geometry question into a picture of the sample space itself.
Most geometry puzzles have one coordinate placement that turns three pages of trigonometry into two lines of algebra. The skill isn't computing, it's noticing which point to put at the origin before you compute anything.
In high dimensions almost all the volume of a solid ball sits in a thin shell near its surface, not near its center, a fact that quietly underlies why high-dimensional data behaves so strangely.
Then the rest