From Peter Mabey
Harlow
Regarding your article on crocheting a hyperbolic plane
(22/29 December, p 38):
in Lewis Carroll’s now-forgotten Sylvie and Bruno Concluded,
chapter 7, “Mein Herr” describes the construction of a “purse” with its outer
surface continuous with its inner one, so that “whatever is outside it is inside
it, so you have all the wealth of the world in it”. This was done by filling in
the opening of a Möbius loop (he refers to it as a Puzzle Ring, as it was
popularly known at the time) with a non-twisted sheet.
I’m not sure whether Carroll was writing before or after Felix Klein’s 1882
publication describing the joining of two Möbius strips. Although the story
wasn’t published till 1889, in the preface Carroll states that he’d started
writing the story in 1873, and most of the substance was in manuscript by
February 1885.
It does seem to be very likely in any case to be the first description of a
one-sided edgeless surface outside the technical literature, unless Carroll had
picked up the idea from Klein in a popular science magazine.
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