August Möbius | |
---|---|

Born | August Ferdinand Möbius 17 November 1790 |

Died | 26 September 1868 77) | (aged

Nationality | Saxon |

Alma mater | University of Leipzig University of Göttingen University of Halle |

Known for | Möbius strip Möbius transformations Möbius transform Möbius function Möbius inversion formula Möbius–Kantor configuration Möbius–Kantor graph |

Scientific career | |

Fields | Mathematician |

Institutions | University of Leipzig |

Doctoral advisor | Johann Pfaff |

Other academic advisors | Carl Friedrich Gauss Karl Mollweide |

Doctoral students | Otto Wilhelm Fiedler |

Other notable students | Hermann Hankel |

**August Ferdinand Möbius** ( UK: /ˈmɜːbiəs/ , US: /ˈmeɪ-,ˈmoʊ-/ ;^{ [1] }German: [ˈmøːbi̯ʊs] ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer.

Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther.^{ [2] } 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.^{ [3] } In 1813, he began to study astronomy under the mathematically inclined professor Carl Friedrich Gauss at the University of Göttingen, 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, where he completed his doctoral thesis *The occultation of fixed stars* in 1815.^{ [3] } In 1816, he was appointed as Extraordinary Professor to the "chair of astronomy and higher mechanics" at the University of Leipzig.^{ [3] } Möbius died in Leipzig in 1868 at the age of 77. His son Theodor was a noted philologist.

He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict Listing a few months earlier.^{ [3] } The Möbius configuration, formed by two mutually inscribed tetrahedra, is also named after him. Möbius was the first to introduce homogeneous coordinates into projective geometry. He is recognized for the introduction of the Barycentric coordinate system.^{ [4] }

Many mathematical concepts are named after him, including the Möbius plane, the Möbius transformations, important in projective geometry, and the Möbius transform of number theory. His interest in number theory led to the important Möbius function 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.^{ [5] }

- 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)

**Johann Carl Friedrich Gauss** was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the *Princeps mathematicorum* and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians.

**Christian Felix Klein** was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time.

**Georg Friedrich Bernhard Riemann** was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as one of the most influential papers in analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time.

**Marius Sophus Lie** was a Norwegian mathematician. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations.

In mathematics, **non-Euclidean geometry** consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either relaxing the metric requirement, or replacing the parallel postulate with an alternative. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry.

**Hermann Minkowski** was a mathematician and professor at Königsberg, Zürich and Göttingen. In different sources Minkowski's nationality is variously given as German, Polish, or Lithuanian-German, or Russian. He created and developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity.

In mathematics, the **Erlangen program** is a method of characterizing geometries based on group theory and projective geometry. It was published by Felix Klein in 1872 as *Vergleichende Betrachtungen über neuere geometrische Forschungen.* It is named after the University Erlangen-Nürnberg, where Klein worked.

**Nikolai Ivanovich Lobachevsky** was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.

**Eduard Study**, more properly **Christian Hugo Eduard Study**, was a German mathematician known for work on invariant theory of ternary forms (1889) and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.

**Johann Friedrich Pfaff** 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 of mathematical thinking, which under Carl Friedrich Gauss and his followers largely determined the lines on which mathematics developed during the 19th century.

**Franz Adolph Taurinus** was a German mathematician who is known for his work on non-Euclidean geometry.

**Friedrich Engel** was a German mathematician.

**Gustav Herglotz** was a German Bohemian physicist. He is best known for his works on the theory of relativity and seismology.

**Paul Gustav Samuel Stäckel** was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term *twin prime* for the first time.

**Johann Christian Martin Bartels** was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan.

**Geometry** is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer.

A timeline of **algebra** and **geometry**

**Ernst Ferdinand Adolf Minding** was a German-Russian mathematician known for his contributions to differential geometry. He continued the work of Carl Friedrich Gauss concerning differential geometry of surfaces, especially its intrinsic aspects. Minding considered questions of bending of surfaces and proved the invariance of geodesic curvature. He studied ruled surfaces, developable surfaces and surfaces of revolution and determined geodesics on the pseudosphere. Minding's results on the geometry of geodesic triangles on a surface of constant curvature (1840) anticipated Beltrami's approach to the foundations of non-Euclidean geometry (1868).

**Ernst Christian Julius Schering** was a German mathematician.

**Hans Wilhelm Eduard Schwerdtfeger** was a German-Canadian-Australian mathematician who worked in Galois theory, matrix theory, theory of groups and their geometries, and complex analysis.

- ↑ Wells, John C. (2008).
*Longman Pronunciation Dictionary*(3rd ed.). Longman. ISBN 978-1-4058-8118-0. - ↑ George Szpiro (2007).
*Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles*. Plume. p. 66. ISBN 978-0-525-95024-0.CS1 maint: discouraged parameter (link) - 1 2 3 4 August Ferdinand Möbius, The MacTutor History of Mathematics archive. History.mcs.st-andrews.ac.uk. Retrieved on 2017-04-26.
- ↑ Hille, Einar. "Analytic Function Theory, Volume I", Second edition, fifth printing. Chelsea Publishing Company, New York, 1982, ISBN 0-8284-0269-8, page 33, footnote 1
- ↑ Howard Eves, A Survey of Geometry (1963), p. 64 (Revised edition 1972, Allyn & Bacon, ISBN 0-205-03226-5)

Wikimedia Commons has media related to August Ferdinand Möbius . |

Wikisource has the text of a 1920 Encyclopedia Americana article about . August Ferdinand Möbius |

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- O'Connor, John J.; Robertson, Edmund F., "August Ferdinand Möbius",
*MacTutor History of Mathematics archive*, University of St Andrews . - August Ferdinand Möbius at the Mathematics Genealogy Project
- 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

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