A 1942 film's throwaway line about a rose hid an exact geometry problem
In the 1942 film Mrs. Miniver, a character describes a rose bred to sit in color exactly between a red circle and a pink one: draw a circle, inscribe the largest equilateral triangle that fits inside it, then inscribe the largest circle that fits inside that triangle. What is the fixed ratio between the two circles' radii, no matter how big the outer circle is?
Reveal the answer
The inner circle's radius is always exactly half the outer circle's — a clean 1:2 ratio, no matter the outer circle's size, because it falls straight out of the fixed relationship between an equilateral triangle's circumradius and inradius. Martin Gardner picked apart the movie's line in his 'Mathematical Games' column and dubbed it the 'Mrs. Miniver problem.'
— Martin Gardner, Mathematical Games: The Mrs. Miniver Problem — Scientific American, 1960s