A stick is broken at random into 3 pieces. It is possible to put them together into the shape of a triangle provided the length of the longest piece is less than the sum of the other 2 pieces; that is, provided the length of the longest piece is less than half the length of the stick. But the probability that a fragment of a stick shall be half the original length of the stick is 1/2. Hence the probability that a triangle can be constructed out of the 3 pieces into which the stick is broken is 1/2.

— Samuel Isaac Jones, Mathematical Wrinkles, 1912

(The actual probability is 1/4.)

from Futility Closet https://www.futilitycloset.com/2019/06/14/a-geometrical-paradox/

Advertisements