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**Ludwig Immanuel Magnus** (March 15, 1790–September 25, 1861) was a German Jewish mathematician who, in 1831, published a paper about the inversion transformation, which leads to inversive geometry.

**Germany**, officially the **Federal Republic of Germany**, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north, and the Alps, Lake Constance and the High Rhine to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, France to the southwest, and Luxembourg, Belgium and the Netherlands to the west.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

In mathematical physics, **inversion transformations** are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time. They are less studied in physics because unlike the rotations and translations of Poincaré symmetry an object cannot be physically transformed by the inversion symmetry. Some physical theories are invariant under this symmetry, in these cases it is what is known as a 'hidden symmetry'. Other hidden symmetries of physics include gauge symmetry and general covariance.

His reputation as a mathematician was established by 1834 and an honorary doctorate conferred on him by the University of Bonn. His work appeared in Gergonne's * Annales de mathématiques pures et appliquées * vols. xi and xvi (1820–25); in * Crelle's Journal *, vols. v, vii, viii, and ix (1830–32); in the third part (1833) of Meier Hirsch's "Sammlung Geometrischer Aufgaben"; and in "Sammlung von Aufgaben und Lehrsätzen aus der Analytischen Geometrie des Raumes" (published in 1837, written earlier).

A **doctorate** or **doctor's degree** or **doctoral degree**, is an academic degree awarded by universities, derived from the ancient formalism *licentia docendi* In most countries, it is a research degree that qualifies the holder to teach at university level in the degree's field, or to work in a specific profession. There are a variety of names for doctoral degrees; the most common is the Doctor of Philosophy (PhD), which is awarded in many different fields, ranging from the humanities to scientific disciplines.

The **University of Bonn** is a public research university located in Bonn, Germany. It was founded in its present form as the Rhein University on 18 October 1818 by Frederick William III, as the linear successor of the Kurkölnische Akademie Bonn which was founded in 1777. The University of Bonn offers a large number of undergraduate and graduate programs in a range of subjects and has 544 professors and 32,500 students. Its library holds more than five million volumes.

* Crelle's Journal*, or just

He studied Euclid while working in his uncle's bank. From 1813 to 1815 he served as a gunner in the Napoleonic Wars. After the war he returned to banking and taught mathematics until 1834, when the founder of the academy at which he was teaching died. He then left teaching and spent nine years as the head revenue officer for the Berliner Kassenverein, retiring in 1843.

**Euclid**, sometimes called **Euclid of Alexandria** to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. His *Elements* is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from the time of its publication until the late 19th or early 20th century. In the *Elements*, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.

**Artillery** is a class of heavy military weapons built to fire munitions far beyond the range and power of infantry's small arms. Early artillery development focused on the ability to breach defensive walls, and fortifications during sieges, and led to heavy, fairly immobile siege engines. As technology improved, lighter, more mobile field artillery cannons developed for battlefield use. This development continues today; modern self-propelled artillery vehicles are highly mobile weapons of great versatility providing the large share of an army's total firepower.

The **Napoleonic Wars** (1803–1815) were a series of major conflicts pitting the French Empire and its allies, led by Napoleon I, against a fluctuating array of European powers formed into various coalitions, financed and usually led by the United Kingdom. The wars stemmed from the unresolved disputes associated with the French Revolution and its resultant conflict. The wars are often categorised into five conflicts, each termed after the coalition that fought Napoleon: the Third Coalition (1805), the Fourth (1806–07), the Fifth (1809), the Sixth (1813), and the Seventh (1815).

**George Pólya** was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians.

**Friedrich Ludwig Gottlob Frege** was a German philosopher, logician, and mathematician. He is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language and mathematics. Though largely ignored during his lifetime, Giuseppe Peano (1858–1932) and Bertrand Russell (1872–1970) introduced his work to later generations of logicians and philosophers.

**Michael Bernays** was born in Hamburg. He studied first law and then literature at Bonn and Heidelberg.

**Heinrich Gustav Magnus** was a notable German experimental scientist. His training was mostly in chemistry but his later research was mostly in physics. He spent the great bulk of his career at the University of Berlin, where he is remembered for his laboratory teaching as much as for his original research. He did not use his first given name, and was known throughout his life as Gustav Magnus.

**Max Wilhelm Dehn** was a German-born American mathematician most famous for his work in geometry, topology and geometric group theory.

**Richard Dagobert Brauer** was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.

**Gustav Leberecht Flügel** was a German orientalist.

**Dan Pedoe** was an English-born mathematician and geometer with a career spanning more than sixty years. In the course of his life he wrote approximately fifty research and expository papers in geometry. He is also the author of various core books on mathematics and geometry some of which have remained in print for decades and been translated into several languages. These books include the three-volume *Methods of Algebraic Geometry*, *The Gentle Art of Mathematics*, *Circles: A Mathematical View*, *Geometry and the Visual Arts* and most recently *Japanese Temple Geometry Problems: San Gaku*.

**Alfred Philippson** was a German geologist and geographer. He was born at Bonn, son of Ludwig Philippson. He received his education at the gymnasium and university of his native town and at the University of Leipzig. In 1892 he became *Privatdozent* at Bonn, was appointed assistant professor seven years later, and in 1904 he was called to Bern as professor of geography. Having made voyages through Italy, Greece, Turkey, and Asia Minor, he published: *Studien über Wasserscheiden,* Berlin, 1886; *Der Peloponnes,* ib. 1892; *Europa*, Leipzig, 1894; *Thessalien und Epirus,* Berlin, 1897; *Beiträge zur Kenntnis der Griechischen Inselwelt,* Gotha, 1901; *Das Mittelmeergebiet,* Leipzig, 1904. He also published essays in the technical journals, such as *Das fernste Italien. Geographische Reiseskizzen und Studien*, Leipzig, 1925, and *Apulien*, Netherlands, 1937.

**Christian Martin Julius Frauenstädt** was a German student of philosophy. He was educated at the house of his uncle at Neisse, and converted from Judaism to Christianity in 1833. Studying theology and, later, philosophy at Berlin, he met Schopenhauer and took up his residence in Berlin in 1848.

**Ernst Fränkel**, **Ernst Fraenkel** German physician (gynecologist). He was the nephew of Ludwig F. Fränkel (1806–1872), German physician.

**Ottomar Ernst Felix Rosenbach** was a German physician.

**Farkas Gyula**, or **Julius Farkas** was a Hungarian mathematician and physicist.

**Charles Taylor** (1840–1908) was an English Christian Hebraist.

**Daniel Christian Ludolph Lehmus** was a German mathematician, who today is best remembered for the Steiner–Lehmus theorem, that was named after him.

**Erich Kamke** was a German mathematician, who specialized in the theory of differential equations. Also, his book on set theory became a standard introduction to the field.

**Ludwig Schlesinger**, was a German mathematician known for the research in the field of linear differential equations.

**Friedrich Dingeldey** was a German mathematician.

**Johann Friedrich Schultz**, also known as **Johann Schultz**, was a German Enlightenment, Protestant, theologian, mathematician and philosopher. He is best known as a close personal friend and trusted expositor of Immanuel Kant. Johann Schultz was a *Hofprediger* and Professor of Mathematics at the University of Königsberg.

*Allg. Deutsche Biographie,*xx.91–92, Leipzig, 1884;- H.S.M. Coxeter (1961)
*Introduction to Geometry*, Chapter 6: Circles and Spheres (pp. 77–95), John Wiley & Sons. - Poggendorff,
*Biog.-Literarisch Handwörterb.*Leipzig, 1863, s.v. ^{article name needed}".*Jewish Encyclopedia*. New York: Funk & Wagnalls Company.

* Allgemeine Deutsche Biographie* is one of the most important and most comprehensive biographical reference works in the German language.

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