Drop a bent wire on a lined floor — does the bend change its odds of crossing a line?
Buffon's needle problem famously shows that dropping a straight needle on a floor of evenly spaced parallel lines lets you estimate pi from how often it crosses a line. Buffon's noodle asks what happens if, instead of a straight needle, you drop a bent wire, or any curve at all, of the same length. Does bending it change the odds of it crossing a line?
Reveal the answer
No. The expected number of crossings depends only on the total length of the curve, not on its shape, a result known as Barbier's theorem after French mathematician Joseph-Émile Barbier, who proved it in 1860. A circle, a zigzag and a straight needle of the same length all cross the lines, on average, exactly the same number of times, which is why the trick still works to estimate pi even with a bent 'noodle.'