Saturday, April 28, 2007

Harmonic Series and Infinite Book Stacking.

There is an awesome illustration of the properties of infinite sets based on harmonic series:

S=1+1/2+1/3+1/4+... (the sum is infinite).

If you have one book of length L, the longest possible overhang is 1/2L (accounting for the gravity). Having two books (of equal size), the longest overhang is (1/2+1/4)L. If you have an infinite number of books, the overhang can be of infinite length. Very neat!

Here are clarifying drawings: http://mathforum.org/advanced/robertd/harmonic.html

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