Carle David Tolmé Runge (August 30, 1856 – January 3, 1927) was a German mathematician, physicist, and spectroscopist. His first name is very often given as Carl. August 30 is the 242nd day of the year in the Gregorian Calendar (243rd in leap years), with 123 days remaining. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... January 3 is the 3rd day of the year in the Gregorian Calendar. ... Events January 7 - First transatlantic telephone call - New York City to London January 9 - Military rebellion crushed in Lisbon January 14 - Paul Doumer elected president of France January 19 - Britain sends troops to China February 12 - First British troops lad on Shanghai February 14 - Earthquake in Yugoslavia - 700 dead February... The Federal Republic of Germany (German: Bundesrepublik Deutschland) is one of the worlds leading industrialised countries, located in the heart of Europe. ... A mathematician is a person whose area of study and research is mathematics. ... The word physicist should not be confused with physician, which means medical doctor. ...

He was co-developer and co-eponym of the Runge-Kutta method, in the field of what is today known as numerical analysis. An eponym is a person (real or fictitious) whose name has become identified with a particular object or activity. ... In numerical analysis, the Runge-Kutta methods are a family of techniques for the approximation of solutions of ordinary differential equations. ... Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ...

He spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864). This article is about the Cuban city. ... For other uses, see Bremen (disambiguation). ... 1864 was a leap year starting on Friday (see link for calendar). ...

In 1880 he received his Ph.D. in mathematics at Berlin, where he studied under Karl Weierstrass. In 1886 he became a professor in Hanover. 1880 was a leap year starting on Thursday (see link for calendar). ... Berlin (pronounced: , German ) is the capital of Germany and its largest city, with 3,387,404 inhabitants (as of September 2004); down from 4. ... Karl Theodor Wilhelm Weierstraß (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. (The letter ß may be transliterated as ss; one often writes Weierstrass. ... 1886 is a common year starting on Friday (click on link to calendar) Events January 18 _ Modern field hockey is born with the formation of The Hockey Association in England. ... Alternate meanings: Hanover (district), Hanover (region), Hanover (state), other uses Map of Germany showing Hanover Hanover (in German: Hannover [haˈnoːfɐ]), on the Leine river, is the capital of the state of Lower Saxony (Niedersachsen) in Germany. ...

His interests included mathematics, spectroscopy, geodesy and astrophysics. In addition to pure mathematics he did a great deal of experimental work studying spectral lines of various elements, and was very interested in the application of this work to astronomical spectroscopy. Spectroscopy is the study of spectra, ie. ... This article or section should include material from Erdmessung. ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties ( luminosity, density, temperature and chemical composition) of astronomical objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies. ... High resolution spectrum of the Sun showing thousands of elemental absorption lines (fraunhofer lines). ...

In 1904 he went to Göttingen, where he remained until he retired in 1925. 1904 is a leap year starting on a Friday (link will take you to calendar). ... Map of Germany showing Göttingen 1 External links Coat of Arms University of Göttingen Top: The old Auditorium Maximum (1862-65) Bottom: New library building Göttingen is a city in Lower Saxony, Germany. ... Events January-May January 3 - Benito Mussolini announces he is taking dictatorial powers over Italy. ...

A crater on the Moon is named after him. The word crater may refer to A landform resembling a pit or depression in the topography that can be formed in several ways: speculation exists that a meteorite impact with another body can cause an impact crater, an electrical discharge on any scale tends to form circular craters, volcanic activity... Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ...

See also:

• Runge's phenomenon
• Runge's method for diophantine equations.

The red curve is the Runge function, the blue curve is a 5th-degree polynomial, while the green curve is a 9th-degree polynomial. ...

External links

• Biography (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Runge.html)
• Biography  (http://numericalmethods.eng.usf.edu/anecdotes/runge.html)

Obituary

• ApJ 69 (1929) 317 (http://adsabs.harvard.edu//full/seri/ApJ../0069//0000317.000.html)