A large panel needs to be moved through a corridor, the panel is tall as the corridor. The corridor is A feet wide before a right angle turn, after the turn, it is B feet wide. What is the maximum length of the panel that can pass through this corner.

Overhead view of the hallway:

+------------+---
|           /   |
|          /    |B ft
|         /     |
|        /+------
|       / |
|      /  |
|     /   |
|    /    |
|   /     |
|  /      |
| /       |
|/        |
+<-A ft-->|

Without the calculus, which corrected the 45-degree assumption, consider geometrically a pivot around the inner corner.  On one side, the increment triangle is long and on the other it's short, so a small change in the angle, producing almost-similar triangles, will affect one side more than the other (one negatively and one positively), so as to leave room for change (and therefore not a min or max).

Posted by Charlie on 2004-05-26 15:55:59