@qed.maths: Break a stick of length 1 at two random points. The pieces x, y, z, with x + y + z = 1, are one point of a triangle. They form a triangle only if each piece is under 1/2 (x < y + z = 1 − x). Three lines x = 1/2, y = 1/2, z = 1/2 cut off three corners: four equal triangles, so the probability is 1/4, not 1/2. 600 real breaks gave 148 triangles (148/600 = 0.247); 6 000 000 gave 0.250. Checked by 23 assertions: exact rational areas, all 179 101 integer breaks of a stick of 600, and Heron's formula on a million random breaks. #math #mathedit #mathanimation #fyp #probability

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Friday 09 October 2026 11:01:55 GMT