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, moons, comets and galaxies – in either ...
.
Early life and education
Möbius was born in
Schulpforta,
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 Charle ...
, 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 Augustinian friar. He is the seminal figure of the Protestant Reformation and the namesake of Lutherani ...
. 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.
[August Ferdinand Möbius, The MacTutor History of Mathematics archive](_blank)
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. From there, he went to study with Carl Gauss's instructor,
Johann Pfaff, 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 ...
in 1868 at the age of 77. His son
Theodor
Theodor is a masculine given name. It is a German form of Theodore. It is also a variant of Teodor.
List of people with the given name Theodor
* Theodor Adorno, (1903–1969), German philosopher
* Theodor Aman, Romanian painter
* Theodor Blueger, ...
was a noted philologist.
Contributions
He is best known for his discovery of the
Möbius strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and A ...
, 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 is ...
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'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...
. It was independently discovered by
Johann Benedict Listing a few months earlier.
The
Möbius configuration, 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 geometr ...
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 ...
.
[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) 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 (incide ...
, the
Möbius transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form
f(z) = \frac
of one complex variable ''z''; here the coefficients ''a'', ''b'', ''c'', ''d'' are complex numbers satisfying ''ad' ...
s, important in projective geometry, and the
Möbius transform 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 integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...
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 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 Uni ...
, 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''
See also
*
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 ...
*
Collineation
*
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 geometr ...
*
Möbius counter
*
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 (incide ...
References
External links
*
*
August Ferdinand Möbius - Œuvres complètesGallica-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