Möbius

August Ferdinand Möbius


Born: 17 Nov 1790 in Schulpforta, Saxony (now Germany)
Died: 26 Sept 1868 in Leipzig, Germany

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August Möbius is best known for his work in topology, especially for his conception of the Möbius strip, a two dimensional surface with only one side.

In 1809 Möbius became a student at Leipzig University. In 1813 he travelled to Göttingen where he studied under Gauss and then he went to Halle where he studied under Johann Pfaff, Gauss's teacher. In 1815 he wrote his doctoral thesis on The occultation of fixed stars and his Habilitation on Trigonometrical equations . In fact while he was writing his thesis there was an attempt to draft him into the Prussian army. Möbius wrote

This is the most horrible idea I have heard of, and anyone who shall venture, dare, hazard, make bold and have the audacity to propose it will not be safe from my dagger.

He avoided the army and was appointed to the chair of astronomy and higher mechanics at the University of Leipzig in 1815 and became director of its observatory in 1848. The observatory had been constructed during the period 1818 to 1821 under Möbius' supervision.

An important work in astronomy concerning occultations of the planets was published in 1815. He also wrote on celestial mechanics.

Möbius's mathematical publications, although not always original, were effective and clear presentations. They are almost all published in Crelle's Journal, the first journal devoted exclusively to publishing mathematics. Möbius's 1827 work on analytical geometry became a classic and includes many of his results in projective and affine geometry.

Möbius' name is attached to many important mathematical objects such as the Möbius function, the Möbius inversion formula and Möbius transformations.

Möbius was a pioneer in topology. In a memoir, presented to the Académie des Sciences and only discovered after his death, he discussed the properties of one-sided surfaces including the Möbius strip which he had discovered in 1858.

A Möbius strip is a two-dimensional surface with only one side. It can be constructed in three dimensions as follows. Take a rectangular strip of paper and join the two end of the strip together so that a band with a 180 degree twist . It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other side of the surface from A.

References elsewhere in this archive:

You can see a picture of a Möbius band

Tell me about Möbius's part in the development of group theory

Tell me about Möbius's work on abstract linear spaces

Tell me about Möbius's work on topology

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. H Gretschel, August Ferdinand Möbius, Archiv der Mathematik und Physik 49 (1869), 1-9.
  4. J Flauvel et al., Möbius and his band (Oxford, 1993).
  5. St-J Kettle, The early life of Möbius and the World in which he lived, in J N Crossley (ed.), First Australian Conference on the History of Mathematics (Clayton, 1981), 145-158.
  6. J-C Pont, La topologie algébrique (Paris, 1974).
  7. H Wussing, Möbius, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).

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JOC/EFR February 1996