This article is from the Puzzles FAQ, by Chris Cole firstname.lastname@example.org and Matthew Daly email@example.com with numerous contributions by others.
A hallway of width A turns through 90 degrees into a hallway of width
B. A ladder is to be passed around the corner. If the movement is
within the horizontal plane, what is the maximum length of the ladder?
------\--------- B / \.......|..B/sin(theta) theta\ | ---|-----X | |\ | | \...|..A/cos(theta) | \ | | \ | | A \|
d(length)/d(theta) = A*sin(theta)/cos(theta)^2 - B*cos(theta)/sin(theta)^2 (?) = 0 A*sin(theta)/cos(theta)^2 = B*cos(theta)/sin(theta)^2 B/A = sin(theta)^3/cos(theta()^3 = tan(theta)^3 theta = inverse_tan(cube_root(B/A))