August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and theoretical

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...

Early life and education

Möbius was born in

Schulpforta Pforta, or Schulpforta, is a school located in Pforta monastery, a former Cistercian monastery (1137–1540), near Naumburg on the Saale River in the German state of Saxony-Anhalt. The site has been a school since the 16th century. Notable past ...

Electorate of Saxony The Electorate of Saxony, also known as Electoral Saxony (German: or ), was a territory of the Holy Roman Empire from 1356–1806. It was centered around the cities of Dresden, Leipzig and Chemnitz. In the Golden Bull of 1356, Emperor Charles ...

, and was descended on his mother's side from religious reformer

Martin Luther Martin Luther (; ; 10 November 1483 – 18 February 1546) was a German priest, theologian, author, hymnwriter, and professor, and Order of Saint Augustine, Augustinian friar. He is the seminal figure of the Reformation, Protestant Refo ...

. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer

Karl Mollweide Karl Brandan Mollweide (3 February 1774 – 10 March 1825) was a German mathematician and astronomer who taught in Halle and Leipzig. In trigonometry, he discovered the formula known as Mollweide's formula. He invented a map projection call ...

.August Ferdinand Möbius, The MacTutor History of Mathematics archive
History.mcs.st-andrews.ac.uk. Retrieved on 2017-04-26. In 1813, he began to study astronomy under mathematician

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

, while Gauss was the director of the

Göttingen Observatory Göttingen Observatory (''Universitätssternwarte Göttingen'' (Göttingen University Observatory) or ''königliche Sternwarte Göttingen'' (Royal Observatory Göttingen)) is a German astronomical observatory located in Göttingen, Lower Saxony, Ge ...

. From there, he went to study with Carl Gauss's instructor,

Johann Pfaff Johann Friedrich Pfaff (sometimes spelled Friederich; 22 December 1765 – 21 April 1825) was a German mathematician. He was described as one of Germany's most eminent mathematicians during the 19th century. He was a precursor of the German school ...

, at the

University of Halle Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university in ...

, where he completed his doctoral thesis ''The occultation of fixed stars'' in 1815. In 1816, he was appointed as Extraordinary Professor to the "chair of astronomy and higher mechanics" at the University of Leipzig. Möbius died in

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as wel ...

in 1868 at the age of 77. His son Theodor was a noted philologist.

Contributions

He is best known for his discovery of the Möbius strip, a

non-orientable In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space i ...

two-dimensional surface with only one side when embedded in three-dimensional

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics ther ...

. It was independently discovered by

Johann Benedict Listing Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician. J. B. Listing was born in Frankfurt and died in Göttingen. He first introduced the term "topology" to replace the older term "geometria situs" (also called ...

a few months earlier. The

Möbius configuration In geometry, the Möbius configuration or Möbius tetrads is a certain configuration in Euclidean space or projective space, consisting of two mutually inscribed tetrahedra: each vertex of one tetrahedron lies on a face plane of the other tetrahed ...

, formed by two mutually inscribed tetrahedra, is also named after him. Möbius was the first to introduce

homogeneous coordinates In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. ...

into

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, ...

. He is recognized for the introduction of the

Barycentric coordinate system In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.). The ba ...

.Hille, Einar. "Analytic Function Theory, Volume I", Second edition, fifth printing. Chelsea Publishing Company, New York, 1982, , page 33, footnote 1 Before 1853 and Schläfli's discovery of the 4-polytopes, Möbius (with Cayley and

Grassmann Hermann Günther Grassmann (german: link=no, Graßmann, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mat ...

) was one of only three other people who had also conceived of the possibility of geometry in more than three dimensions. Many mathematical concepts are named after him, including the

Möbius plane In mathematics, a Möbius plane (named after August Ferdinand Möbius) is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane. The classical example is based on the geometry of lines and circles in the real affine plane. A s ...

, the Möbius transformations, important in projective geometry, and the

Möbius transform Moebius, Möbius or Mobius may refer to: People * August Ferdinand Möbius (1790–1868), German mathematician and astronomer * Theodor Möbius (1821–1890), German philologist * Karl Möbius (1825–1908), German zoologist and ecologist * Pau ...

of number theory. His interest in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

led to the important

Möbius function The Möbius function is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated ''Moebius'') in 1832. It is ubiquitous in elementary and analytic number theory and most of ...

μ(''n'') and the

Möbius inversion formula In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius. A large gener ...

. In Euclidean geometry, he systematically developed the use of signed angles and line segments as a way of simplifying and unifying results.

Howard Eves Howard Whitley Eves (10 January 1911, New Jersey – 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics. Eves received his B.S. from the University of Virginia, an M.A. from Harvard Universi ...

, A Survey of Geometry (1963), p. 64 (Revised edition 1972, Allyn & Bacon, )

Collected works

Gesammelte Werke erster Band (v. 1)
(Leipzig : S. Hirzel, 1885)
Gesammelte Werke zweiter Band (v. 2)
(Leipzig : S. Hirzel, 1885)
Gesammelte Werke dritter Band (v. 3)
(Leipzig : S. Hirzel, 1885)
Gesammelte Werke vierter Band (v. 4)
(Leipzig : S. Hirzel, 1885)
Die elemente der mechanik des himmels, auf neuem wege ohne hülfe höherer rechnungsarten dargestellt von August Ferdinand Möbius
(Leipzig, Weidmann'sche buchhandlung, 1843) File:Mobius-1.jpg, 1843 copy of ''Die Elemente der Mechanik des Himmels'' File:Mobius-2.jpg, Title page to a 1843 copy of ''Die Elemente der Mechanik des Himmels'' File:Mobius-3.jpg, First page to a 1843 copy of ''Die Elemente der Mechanik des Himmels''

References

External links

* *
August Ferdinand Möbius - Œuvres complètes
Gallica-Math * A beautiful visualization of Möbius Transformations, created by mathematicians at the University of Minnesota is viewable at https://www.youtube.com/watch?v=JX3VmDgiFnY {{DEFAULTSORT:Mobius, August Ferdinand 1790 births 1868 deaths People from Naumburg (Saale) 19th-century German astronomers 19th-century German mathematicians Number theorists Geometers Leipzig University alumni University of Göttingen alumni University of Halle alumni Leipzig University faculty

Early life and education

Contributions

Collected works

See also

References

External links