August Mobius

August Ferdinand Möbius or Moebius (/ˈʔaʊgʊst ˈfɛɐdiːnant ˈmøːbjʊs / Schulpforta, November 17, 1790-Leipzig, September 26, 1868) was a German mathematician and theoretical astronomer.

Biography

Möbius was born in the Schulpforta College (Saxony-Anhalt), where his father Johann Heinrich Möbius (1742-1792) taught dance. His mother, Johanne Katharine Christiane Keil (1756-1820), was a seventh-generation descendant of the religious reformer Martin Luther. Since her husband died when her only child was three years old, it was she who educated him until he was thirteen, the age at which he entered the Schulpforta school.

Although he started Law in Leipzig (1809) to please his family, he left it after the semester for his great passion: science. He studied mathematics, astronomy and physics at different universities and with famous scientists of his time, especially astronomy in Leipzig with Karl Mollweide, a subject that he expanded in Göttingen under the supervision of Carl Friedrich Gauss. In Halle he was taught by Johann Friedrich Pfaff, who directed his thesis, read in 1815, De computandis occultationibus fixarum per planetas on calculation methods applied to the study of fixed stars hidden by planets. In that same year he wrote his habilitation thesis on trigonometric equations. In 1816, the Prussian army tried to recruit him, but managed to prevent it.

Gauss recommended him in 1816 to be extraordinary professor of the Chair of Astronomy and Higher Mechanics at the University of Leipzig, replacing his teacher Mollweide. He taught there and in 1844 he was made a professor. In 1846 he was also elected a member of the Göttingen Academy of Sciences and from 1848 he was director of the Leipzig Observatory, whose reconstruction he had supervised. Almost all of his work was published in Crelle, the first journal devoted exclusively to research articles in mathematics.

Möbius married Dorothea Rothe (1790-1859), daughter of a surgeon, in 1820, from whom he had three children: August (1821-1890), Emilie (1822-1897) and Paul (1825-1889). The latter gave him five grandchildren, one of whom was the famous neurologist Paul Julius Möbius (1853-1907), known for his research on Möbius syndrome.

He is best known for his discovery in 1858 of the Möbius band together with the German mathematician Johann Benedict Listing. It is a non-orientable two-dimensional surface with only one side when immersed in three-dimensional Euclidean space. Instructions for building it, together with some description of its topological properties, were found in a memoir submitted by Möbius to the French Académie des Sciences some time after his death in Leipzig. Today his invention has generated numerous industrial designs: conveyor belts for hot materials, abrasive belts or ink cartridges with the shape of a Möbius strip instead of a cylindrical one, which last twice as long when its only face is optimally used.

Moebius tape

Möbius was the first to introduce homogeneous coordinates in projective geometry. The Möbius transformation, important in projective geometry, should not be confused with the Möbius transform, used in number theory, which likewise bears his name. He was also interested in number theory; the important Möbius arithmetic function μ(n) and the Möbius inversion formula are named after him.

Eponymy

In addition to the different mathematical and geometric concepts that bear his name:

• The lunar crater Möbius carries this name in his memory.
• The asteroid (28516) Möbius also commemorates its name.