Look Before You Leap

Too predictable?

Why do frogs, kangaroos, lords and leopards like 2012?
Because it’s a leap year!
(Did you know that a group of leopards is called a “leap”?)

Speaking of leaps, a friend and I were recently discussing the following problem:

A flea can jump up to 350 times its own length. If the same were true of humans, how far would a person whose height is 5′ 6″ be able to jump?

Though the intent is clear, the problem assumes that the length of a flea is analogous to the height of a human. A would-be solver who overthinks this problem might reason that a flea’s length is approximately twice its height, in which case it could jump 350 × length = 350 × (2 × height) = 700 times its own height. Solving the proportion required by the problem, a 5′ 6″ human would be able to jump 3,850 feet, which is twice the intended answer.

Not that it matters. Even long jumper Mike Powell, who holds the world record with a jump of 29′ 4″, was not able to leap even five times his height.

But the problem reminded me of this joke…

A team of engineers was required to measure the height of a flag pole. They only had a measuring tape, and they were frustrated that they couldn’t slide the tape up the pole. After a while, a mathematician happens by, hears about their problem, removes the pole from the ground, and proceeds to measure it easily.

When he leaves, one engineer says, “That is just like a mathematician! We need to know the height, and he gives us the length!”