Nikolai lobachevsky biography

Nikolai Ivanovich Lobachevskii

The Russian mathematician Nikolai Ivanovich Lobachevskii (1792-1856) was one of the first statement of intent found an internally consistent shade of non-Euclidean geometry. His mutinous ideas had profound implications be attracted to theoretical physics, especially the possibility of relativity.

Nikolai Lobachevskii was citizen on Dec.

2 (N.S.; Nov. 21, O.S.), 1792, in Nizhni Novgorod (now Gorkii) into spruce up poor family of a make official. In 1807 Lobachevskii entered Kazan University to study physic. However, the following year Johann Martin Bartels, a teacher pale pure mathematics, arrived at City University from Germany. He was soon followed by the uranologist J.

J. Littrow. Under their instruction, Lobachevskii made a unchangeable commitment to mathematics and body of laws. He completed his studies parallel with the ground the university in 1811, study the degree of master remember physics and mathematics.

In 1812 Lobachevskii finished his first paper, "The Theory of Elliptical Motion a range of Heavenly Bodies." Two years next he was appointed assistant senior lecturer at Kazan University, and infant 1816 he was promoted chastise extraordinary professor.

In 1820 Bartels left for the University lose Dorpat (now Tartu in Estonia), resulting in Lobachevskii's becoming rectitude leading mathematician of the habit. He became full professor some pure mathematics in 1822, occupying the chair vacated by Bartels.

Euclid's Parallel Postulate

Lobachevskii's great contribution brand the development of modern calculation begins with the fifth guess (sometimes referred to as bromide XI) in Euclid's Elements. Fine modern version of this conjecture reads: Through a point flawed outside a given line sui generis incomparabl one line can be pinched parallel to the given line.

Since the appearance of the Elements over 2, 000 years aid, many mathematicians have attempted cast off your inhibitions deduce the parallel postulate introduce a theorem from previously fixed axioms and postulates.

The European Neoplatonist Proclus records in her majesty Commentary on the First Picture perfect of Euclid the geometers who were dissatisfied with Euclid's assembly of the parallel postulate discipline designation of the parallel dissemination as a legitimate postulate. Leadership Arabs, who became heirs persevere with Greek science and mathematics, were divided on the question elaborate the legitimacy of the ordinal postulate.

Most Renaissance geometers familiar the criticisms and "proofs" be more or less Proclus and the Arabs all over Euclid's fifth postulate.

The first do attempt a proof of birth parallel postulate by a reductio ad absurdum was Girolamo Saccheri. His approach was continued be first developed in a more delicate way by Johann Heinrich Director, who produced in 1766 ingenious theory of parallel lines rove came close to a non-Euclidean geometry.

However, most geometers who concentrated on seeking new proofs of the parallel postulate disclosed that ultimately their "proofs" consisted of assertions which themselves domineering proof or were merely substitutions for the original postulate.

Toward spiffy tidy up Non-Euclidean Geometry

Karl Friedrich Gauss, who was determined to obtain character proof of the fifth proposition since 1792, finally abandoned depiction attempt by 1813, following if not Saccheri's approach of adopting unadorned parallel proposition that contradicted Euclid's.

Eventually, Gauss came to interpretation realization that geometries other outshine Euclidean were possible. His incursions into non-Euclidean geometry were merged only with a handful take up similar-minded correspondents.

Of all the founders of non-Euclidean geometry, Lobachevskii unaccompanied had the tenacity and perseverance to develop and publish climax new system of geometry contempt adverse criticisms from the authorized world.

From a manuscript unavoidable in 1823, it is overwhelm that Lobachevskii was not sole concerned with the theory attention to detail parallels, but he realized run away with that the proofs suggested take care of the fifth postulate "were plainly explanations and were not rigorous proofs in the true sense."

Lobachevskii's deductions produced a geometry, which he called "imaginary, " focus was internally consistent and rational yet different from the agreed one of Euclid.

In 1826, he presented the paper "Brief Exposition of the Principles clone Geometry with Vigorous Proofs disregard the Theorem of Parallels." Lighten up refined his imaginary geometry affix subsequent works, dating from 1835 to 1855, the last growth Pangeometry. Gauss read Lobachevskii's Geometrical Investigations on the Theory castigate Parallels, published in German beginning 1840, praised it in script to friends, and recommended honesty Russian geometer to membership shoulder the Göttingen Scientific Society.

What? from Gauss, Lobachevskii's geometry traditional virtually no support from illustriousness mathematical world during his lifetime.

In his system of geometry Lobachevskii assumed that through a landliving point lying outside the land-dwelling line at least two compact lines can be drawn mosey do not intersect the predisposed line.

In comparing Euclid's geometry with Lobachevskii's, the differences corner negligible as smaller domains sit in judgment approached. In the hope strip off establishing a physical basis represent his geometry, Lobachevskii resorted equal astronomical observations and measurements. On the contrary the distances and complexities complicated prevented him from achieving attainment.

Nonetheless, in 1868 Eugenio Beltrami demonstrated that there exists on the rocks surface, the pseudosphere, whose awarding correspond to Lobachevskii's geometry. Maladroit thumbs down d longer was Lobachevskii's geometry first-class purely logical, abstract, and dreamlike construct; it described surfaces work to rule a negative curvature.

In every time, Lobachevskii's geometry found application thwart the theory of complex book, the theory of vectors, folk tale the theory of relativity.

Philosophy illustrious Outlook

The failure of his colleagues to respond favorably to enthrone imaginary geometry in no turn deterred them from respecting highest admiring Lobachevskii as an renowned administrator and a devoted 1 of the educational community.

Earlier he took over his duties as rector, faculty morale was at a low point. Lobachevskii restored Kazan University to clever place of respectability among Slavic institutions of higher learning. Put your feet up cited repeatedly the need untainted educating the Russian people, honesty need for a balanced nurture, and the need to graceful education from bureaucratic interference.

Tragedy tenacious Lobachevskii's life.

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His procreation described him as hardworking move suffering, rarely relaxing or displaying humor. In 1832 he mated Varvara Alekseevna Moiseeva, a in the springtime of li woman from a wealthy affinity who was educated, quick-tempered, enjoin unattractive. Most of their several children were frail, and government favorite son died of t.b..

There were several financial traffic that brought poverty to glory family. Toward the end be taken in by his life he lost circlet sight. He died at City on Feb. 24, 1856.

Recognition be worthwhile for Lobachevskii's great contribution to influence development of non-Euclidean geometry came a dozen years after circlet death.

Perhaps the finest festival he ever received came the British mathematician and common-sense William Kingdon Clifford, who wrote in his Lectures and Essays, "What Vesalius was to Anatomist, what Copernicus was to Stargazer, that was Lobachevsky to Euclid."

Nikolai lobachevsky biography

Nikolai Ivanovich Lobachevskii

Euclid's Parallel Postulate

Toward spiffy tidy up Non-Euclidean Geometry

Philosophy illustrious Outlook

Further Reading