A tower, 200 feet high, has an elevator inside it, and a spiral stairway winding its way around the tower at a constant 30 degree angle with the horisontal.

Given the tower's radius of 10 feet, what is the difference between the distance covered by a person going up in the elevator, versus one climbing the stairs?

Richard's method is incorrect.. the spiral staircase's length is found the same way as engineers do screw calculations -- you "unwind" the screw's pitch into a triangle -- the hypotenuse represents the path along one revolution of the spiral. The leg opposite the pitch angle represents the vertical distance, or that of the elevator ride.

In this case it's a nice neat 30/60/90 triangle, so the ratio of the leg opposite the 30 degree angle to the hypotenuse (ie, the distance traveled on the elevator to that on the stairs) is 2*sqrt(2), or 2.818; so the stair walker travels 563.6 feet, 363.6 feet further.

Posted by nate on 2002-05-07 04:07:14