Nikolay Ivanovich Lobachevsky

Nikolai Ivanovich Lobachevsky (Никола́й Ива́нович Лобаче́вский) (December 1, 1792–February 24, 1856 (N.S.); November 20, 1792–February 12, 1856 (O.S.)) was a Russian mathematician. Pic of a 19th century painting. ... Pic of a 19th century painting. ... December 1 is the 335th (in leap years the 336th) day of the year in the Gregorian calendar. ... 1792 was a leap year starting on Sunday (see link for calendar). ... February 24 is the 55th day of the year in the Gregorian Calendar. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... The Gregorian calendar is the most widely used calendar in the world. ... November 20 is the 324th day of the year (325th in leap years) in the Gregorian Calendar. ... 1792 was a leap year starting on Sunday (see link for calendar). ... February 12 is the 43rd day of the year in the Gregorian Calendar. ... 1856 was a leap year starting on Tuesday (see link for calendar). ... The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ...

Biography

Lobachevsky was born in Nizhny Novgorod, Russia. His parents were Ivan Maksimovich Lobachevsky, a clerk in a landsurveying office, and Praskovia Alexandrovna Lobachevskaya. In 1800, his father died and his mother moved to Kazan. In Kazan, Nikolai Ivanovich Lobachevsky attended Kazan Gymnasium, graduating in 1807 and then Kazan University which was founded just three years earlier, in 1804. Nizhny Novgorod (Russian: ), colloquially shortened as Nizhny and also transliterated into English as Nizhniy Novgorod or Nizhni Novgorod or Nizhnii Novgorod, is the fourth largest city of Russia, ranking after Moscow, St. ... Surveyor at work with a leveling instrument. ... Kazan (Russian: ; Tatar: Qazan, Казан) is the capital city of the Republic of Tatarstan, Russia, and one of Russias largest cities. ... Kazan Gymnasium was a Gymnasium of Kazan city. ... The main bulding of the university, 19th century Kazan State University is located in Kazan, Tatarstan, Russia. ...

At Kazan University, Lobachevsky was influenced by professor Johann Christian Martin Bartels (1769–1833), a former teacher and friend of German mathematician Carl Friedrich Gauss. Lobachevsky received a Master's degree in physics and mathematics in 1811. In 1814, he became a lecturer at Kazan University, and in 1822 he became a full professor. He served in many administrative positions and was the rector of Kazan University from 1827 to 1846. He retired (or was dismissed) in 1846, after which his health rapidly deteriorated. In addition to teaching mathematics and physics at Kazan University Lobachevsky also was an astronomy teacher there.   (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ... A masters degree is an academic degree usually awarded for completion of a postgraduate (or graduate) course of one to three years in duration. ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time and explaining them using mathematics. ... A professor giving a lecture The meaning of the word professor (Latin: one who claims publicly to be an expert) varies. ... The word rector (ruler, from the Latin regere) has a number of different meanings. ...

In 1832, he married Varvara Alexivna Moisieva. They had seven children.

Mathematical results

Lobachevsky's main achievement is the development (independently from János Bolyai) of non-Euclidean geometry. Before him, mathematicians were trying to deduce Euclid's fifth postulate from other axioms. Euclid's fifth is a rule in Euclidean geometry which states (in Playfair's John Playfair reformulation) that for any given line and point not on the line, there is one parallel line through the point not intersecting the line. Lobachevsky would instead develop a geometry in which the fifth postulate was not true. This idea was first reported on February 23 (Feb. 11, O.S.), 1826 to the session of the department of physics and mathematics, and this research was printed in the UMA (Вестник Казанского университета) in 1829–1830. Lobachevsky wrote a paper about it called A concise outline of the foundations of geometry that was published by the Kazan Messenger but was rejected when the St. Petersburg Academy of Sciences submitted it for publication. This non-Euclidean geometry that Lobachevsky developed was called hyperbolic geometry. Lobachevsky replaced Euclid's parallel postulate with the postulate that there is more than one parallel line through any given point; a famous consequence is that the sum of angles in a triangle must be less than 180 degrees. The recognition of his ideas by the mathematical community was quite slow. Some mathematicians and historians have claimed that Lobachevsky stole his concept of non-Euclidean geometry from Gauss, but this is not true because Lobachevsky was not corresponding with Gauss at the time, Lobachevsky deserves full credit for inventing non-Euclidean geometry.[1] These ideas were fully accepted only several decades after Lobachevsky's death. But non-Euclidean geometry turned out to be very important for mathematics and science; the German physicist Albert Einstein used a generalization of it for his theory of general relativity. Lobachevsky's magnum opus Geometriya was completed in 1823, but was not published in its exact original form until 1909, long after he had passed away. Lobachevsky was also the author of New Foundations of Geometry (1835-1838). He also wrote Geometrical Investigations on the Theory of Parallels (1840) and Pangeometry (1855). János Bolyai (December 15, 1802–January 27, 1860) was a Hungarian mathematician. ... Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes hyperbolic, elliptic and absolute geometry, which are contrasted with Euclidean geometry. ... Euclid (Greek: ), also known as Euclid of Alexandria, was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BC). ... In geometry, the parallel postulate, also called Euclids fifth postulate since it is the fifth postulate in Euclids Elements, is a distinctive axiom in what is now called Euclidean geometry. ... This article does not cite its references or sources. ... Professor John Playfair FRSE (March 10, 1748 – July 20, 1819) was a Scottish scientist. ... Table of Geometry, from the 1728 Cyclopaedia. ... February 23 is the 54th day of the year in the Gregorian Calendar. ... Old Style can refer to: Old Style and New Style dates, a shift from the Julian to the Gregorian calendar: in Britain in 1752, in Russia in 1918. ...

Another of Lobachevsky's achievements was developing a method for the approximation of the roots of algebraic equations. This method is now known as Dandelin-Gräffe method, named after two other mathematicians who discovered it independently. In Russia, it is called the Lobachevsky method. Lobachevsky gave the definition of a function as a correspondence between two sets of real numbers (Dirichlet gave the same definition independently soon after Lobachevsky). It has been suggested that this article or section be merged with estimation. ... In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that f(x) = 0. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... Graeffes method is an algorithm for finding multiple roots of a polynomial. ... Partial plot of a function f. ... Peter Gustav Lejeune Dirichlet. ...

In popular culture

In the 1950s, humorist, satirist, and mathematician Tom Lehrer wrote a song, inspired by a Danny Kaye routine about Stanislavsky, in which he credited Lobachevsky with teaching him the secret of success as a mathematician: plagiarism ("Plagiarize! Let no one else's work evade your eyes! Remember why the Good Lord made your eyes, don't shade your eyes, but plagiarize! Plagiarize! Plaagiarize! Only be sure always to call it, please, 'research.'!") Lehrer chose Lobachevsky mainly because his name was reminiscent of Stanislavsky's, and not because Lobachevsky is particularly known for this misdemeanor. Look up Humour in Wiktionary, the free dictionary. ... 1867 edition of the satirical magazine Punch, a British satirical magazine, ground-breaking on popular literature satire. ... Tom Lehrer in 1960. ... Kaye entertaining U.S. troops at Sasebo, Japan, 25 Oct 1945 David Daniel Kaminsky, known as Danny Kaye (January 18, 1913 – March 3, 1987) was an American actor, singer and comedian. ... Konstantin (Constantin) Stanislavski (Константи́н Серге́евич Станисла́вский / Алексе́ев) (January 5, 1863... Plagiarism is the unauthorized use or close imitation of the language and thoughts of another author and the representation of them as ones own original work. ...

In Poul Anderson's novella "Operation Changeling" (F&SF, 1969; Operation Chaos, 1971), a group of sorcerers navigate a non-Euclidean universe with the assistance of the ghosts of Lobachevsky and Bolyai. (The novella also makes a reference to Lehrer's song.) Poul Anderson portrayed on the cover of a special edition of The Magazine of Fantasy and Science Fiction; painting by Kelly Freas. ... A novella is a narrative work of prose fiction somewhat longer than a short story but shorter than a novel. ... F&SF April 1971, special Poul Anderson issue. ... For the CIA intelligence project, see Operation CHAOS. Operation Chaos is a 1971 science fiction/fantasy fixup novel by Poul Anderson. ...

See also

• Non-Euclidian geometry
• Hyperbolic geometry
• Hyperboloid structure
• Gauss-Bolyai-Lobachevsky space
• Upper half-plane
• Lobachevskiy (crater)
• Lobachevsky Medal

The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Lines through a given point P and hyperparallel to line l. ... The worlds first hyperboloid water tower by Vladimir Shukhov, All-Russian Exposition, Nizhny Novgorod, Russia, 1896 Hyperboloid structures in architecture were first applied by Russian engineer Vladimir Shukhov (1853-1939). ... Gauss-Bolyai-Lobachevsky space is a non-Euclidean space with a negative Gaussian curvature — that is, a hyperbolic geometry. ... In mathematics, the upper half plane H is the set of complex numbers x + iy such that y > 0. ... Lobachevsky is a lunar impact crater that is located on the far side of the Moon, beyond the eastern limb. ... Lobachevsky Medal (Lobachevsky International Prize) is a medal awarded by Kazan University in honor of Nikolai Ivanovich Lobachevsky, who was a professor there. ...

External links

• O'Connor, John J., and Edmund F. Robertson. "Nikolai Ivanovich Lobachevsky". MacTutor History of Mathematics archive.
• Lobachevsky song by Tom Lehrer, in MP3 format.
• [2] Web site dedicated to Lobachevsky (in Spanish).