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-->|

The proof may be shortened. In the third paragraph where it reads "we eventually get to (x-b)³+a²(x-b)-a²x=0" you can simplify and get "(x-b)³-a²b=0" and thus find x directly without introducting z at all.

Posted by e.g. on 2004-05-27 10:02:20