Science Behind Things

Math Trivia Question

July 24, 2007 on 8:46 pm | In Math Trivia | 9 Comments

A new friend of mine named Hao (pronounced “How”) gave me this math puzzle, which he, Stephen, Stephen’s brother Chris and I then solved. Can you solve it? I’ll give the solution in a few days, but I’d like to hear from you if you can solve it.

Imagine a 1 by 1 box. The diagonal within that box from one corner to the opposite corner is exactly the square root of 2, or about 1.4142135623730950488016887242097 (or about 1.4). Furthermore, imagine another 1 x 1 box, and a “staircase” going from one corner to the opposite corner. As the steps get smaller and smaller, heading toward an infinite number of steps, consisting of tiny vertical and tiny horizontal lines, each adding up to a height of exactly one unit and a width of exactly one unit, the total distance is exactly 2. Why is it not approaching 1.4?

Tell me the answer, if you can figure it out.