## EMS: The Möbius Surface

**A Mathematical Curiosity**

Properties of a "Möbius Surface"

Properties of a "Möbius Surface"

A peculiar configuration known as a "Möbius Surface" figured in a paper read last night at a meeting of the Edinburgh Mathematical Society in the Mathematical Institute, Chambers Street, Edinburgh.

It was explained that to make a Möbius surface one took a strip of paper and pinned the ends together, as if making a serviette ring, but first giving the strip a single twist. Unlike a serviette ring, the surface so formed has only one continuous edge; but its more surprising property was that it possesses only one side. A caterpillar crawling on it could start from any point and find himself later at the same point on the other side of the paper, never having crossed the edge.

The paper was entitled, "Some properties of points on a singly-twisted "Möbius surface," and was read in collaboration by Dr W O Kermack and Lieut.-Colonel A G McKendrick. Small paper models were handed round to the audience, and a large model showed what the surface became when deformed in such a way that the single edge became a circle. The authors dealt with the statistical properties of certain distributions of points on the Möbius surface. In the discussion that followed, Dr A C Aitken stated that the conceptions introduced by the authors were likely to be of great value to statisticians; and Professor M Born described some important problems arising in physics which might be tackled on similar lines.

Other papers of the programme were: *Deformable quadrics and their circular sections*, by Professor H W Turnbull, F.R.S., illustrated with a series of folding cardboard models; *A note on the history of the fundamental theorem of the integral calculus*, in which Professor Turnbull showed that an important theorem, commonly ascribed to Barrow in 1669, was actually contained in Gregory's *Pars Universalis* (1668), and should therefore be credited to the latter mathematician; *On the intersection of certain quadrics*, by L M Brown; and *On the projective geometry of paths*, by Dr J Haantjes.

JOC/EFR May 2016

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http://www-history.mcs.st-andrews.ac.uk/Extras/ems_Mobius.html