According to legend, the purse of Fortunatus continually replenished itself as coins were withdrawn from it.
A story by Lewis Carroll (Charles L. Dodgson) describes how to make such a purse from four handkerchiefs. The resulting form is a model of a topological structure known as the projective plane.
A projective plane can be constructed by gluing both pairs of opposite edges of a rectangle together giving both pairs a half-twist. It is a one-sided surface, but cannot be realized in three-dimensional space without crossing itself.
Creating a model of Fortunatus's Purse presents an interesting challenge for both artisans and mathematicians.
Photos by I. Peterson
1 comment:
the story, chapter 7 of sylvie and bruno concluded, has a character known as "mein herr" instructing his longtime friend, lady muriel, on the creation of a fortunatus purse using 3 pocket handkerchiefs, not 4. the only problem with the offered description both here & there is the lack of visual aid (putting aside the illustration showing the handkerchiefs held up by mein herr), without actually attempting to construct one yourself. the photos of the ones created by ms. goldstein don't really illustrate the concept very well either, unfortunately, so we're left with a rather interesting rainy day project!
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