A Rope, Two Telephone Poles... and Some Confounding Math

Apr 16, 2011

RAY: There are two telephone poles. Each one is 100-feet tall. They are parallel and an unknown distance apart.

We're going to attach a 150-foot rope from the very top of one of the poles to the top of the other. This rope will, of course, droop down somewhat. That drooping rope is called a catanary, from the Latin word for chain.

The question is: What must be the distance between the two poles, so that the lowest point of the catanary is 25-feet above the ground?

RAY: The question was: What must the distance be between the two poles so that the lowest point of this catenary is 25 feet above the ground?

If you made the mistake that I made and you drew the picture, and then went immediately and started to look up what the equation for a catenary was, you weren't going to get the answer.

But if you thought about it for a little longer you would realize that it's impossible for that rope to get down to 25 feet above the ground, unless the two poles are touching each other.

TOM: I'll bet you all the little nerds went right to their graphing calculators. What a dirty trick!

RAY: I'm sorry. It was a dirty trick. It wasn't really a mathematical puzzler.
Do we have a winner?

TOM: The winner is Kirsten Gilbert from Winter Park, Florida.

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