Posted by: Dave Richeson | September 14, 2008

Does gold tarnish? The golden spiral and nautilus shells.

I jotted down notes all summer in preparation for an entertaining article that I hoped to write for an undergraduate journal like Mathematics Magazine, College Mathematics Journal, The Mathematical Intelligencer, etc.  It had the working title “Mythematics.”  The idea would be to state several famous mathematical myths and either debunk them or argue for their veracity (inspired by the Mythbusters TV show).

Some examples are the myths that there is no Nobel Prize in mathematics because a mathematician had an affair with Nobel’s wife (not true), the Bible says \pi=3 (essentially true), and that the young Gauss amazed his teacher by summing 1 to 100 (sort of true).

Well, summer slipped away and the article didn’t get written (although I’m still planning to do so). When I do I will certainly include the many glorious myths about the golden ratio and the Fibonacci numbers in art, architecture, and nature. Most of these were soundly debunked by George Markowsky in his article “Misconceptions of the Golden Ratio” (in the January 1992 issue of the College Mathematics Journal). However, the myths seem to live on.  As Underwood Dudley wrote in his scathing review of The (Fabulous) Fibonacci Numbers, “I would say that [Markowsky] had done it [debunked the myths] once and for all, but the truth is sometimes slow to catch up with gee-whiz stories.” (My hunch is that the staying-power of these myths is due to their presence in the 1959 cartoon Donald in Mathemagic Land, which, if my childhood was typical, most schoolchildren watch every year for several years in their math classes.)

Today God Plays Dice wrote about a year-and-a-half old blog posting by Shallow Thoughts in which Shallow Thoughts discovered that the nautilus shell does not have the shape of the “golden” logarithmic spiral (he has a nice photo to illustrate this). God Plays Dice points out that this was known already.

It looks like I have one more item to add to my list of myths.  Now I just have to find the time to write the article…

Have a favorite mathematical myth (whether true or false)?  Share it in the comments.

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