August Möbius dies

August Ferdinand Möbius died in Leipzig on September 26, 1868, at the age of 77. He had spent most of his working life at the University of Leipzig, where he was appointed in 1816 to the chair of astronomy and higher mechanics. Although he trained and worked as a theoretical astronomer, he is remembered chiefly as a mathematician. Through his mother, he was a descendant of the religious reformer Martin Luther.

Möbius was born on November 17, 1790, in Schulpforta, in the Electorate of Saxony. He was taught at home until 13, then attended the college in his hometown until 1809. At Leipzig he studied astronomy with Karl Mollweide. In 1813 he moved to Göttingen to learn from Carl Friedrich Gauss, who directed the observatory there, and he went on to Halle to work with Johann Pfaff, Gauss’s own former teacher. He finished his doctoral thesis, on the occultation of fixed stars, in 1815.

His best-known discovery is the strip that bears his name: a surface with only one side, which anyone can make by joining the ends of a paper strip after giving it a half-twist. Möbius described it in 1858. Johann Benedict Listing found the same object independently, a few months earlier.

Why it matters

The strip is only part of his legacy. Möbius introduced homogeneous coordinates into projective geometry and is credited with the barycentric coordinate system. In Euclidean geometry he developed the systematic use of signed angles and line segments, which simplified many results. He was also one of the few people of his time who imagined geometry in more than three dimensions.

Many concepts carry his name, among them Möbius transformations, the Möbius plane, and the Möbius function and inversion formula in number theory. His son Theodor became a noted philologist, and his collected works were published in four volumes in 1885.

Did you know?

Long before Möbius and Listing described it mathematically, the one-sided strip appeared in Roman mosaics from the third century CE.