Then when I went to work at the Franklin Institute in 1970 one of my first jobs was to manage the production of a small math exhibit. Given the very modest funding available, we decided that most of the hands-on activities would be adapted from existing math puzzles. They are very inexpensive to build and maintenance costs are very low. Some ask if they can buy a copy of the puzzle. Surely our visitors are enjoying the challenge of trying to solve the puzzle.
Many math puzzles exemplify important mathematics.
Such is the case with Harmonic Cantilever. The harmonic sequence was first studied about 2,500 years ago by Pythagoras and his followers. If the mass and the tension of the string is fixed, these lengths correspond to musical relationships now known as the octave, the fifth above the octave, the second octave, and the third above the second octave. If played simultaneously, these notes will sound as a familiar major chord, spread out over two octaves. The terms of the harmonic sequence get smaller, approaching zero.