Wednesday, June 08, 2005

Beam Detector

Here's a problem posed to an interviewed canditate to a NY financial firm. I have rephrased the problem because the initial statement is terrible:

Given a circle of radius 1 and a line that intersects the circle, find the minimum length of any curve (or set of curves) that guarantees that these curves will intersect the line.

For example, a curve that consists of the circumference of the circle will intersect the line for sure, but it will have a length of 2π. The best solution using one curve is π+2=5.14, and the proved lower limit is π.