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Janos Bolyai

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Nikolai Lobachevsky – The Copernicus of Geometry

Nikolai Lobachevsky – The Copernicus of Geometry

Harald Sack
On February 24, 1856, Russian mathematician and geometer Nikolai Ivanovich Lobachevsky passed away. He is known primarily for his work on hyperbolic geometry. Lobachevsky’s main achievement is the development (independently from János Bolyai) of a non-Euclidean geometry, also referred to as Lobachevskian geometry. Nikolai Lobachevsky – Early Years Nikolai Lobachevsky was born as one of three children either in or near the city of Nizhny Novgorod in Russia in 1792 to parents…
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mathematics
Janos Bolyai and the Discovery of Non-Euclidian Geometry

Janos Bolyai and the Discovery of Non-Euclidian Geometry

Harald Sack
On December 15, 1802, Hungarian mathematician János Bolyai was born. He is most famous for being one of the founders of non-euclidian geometry, a geometry that differs from Euclidean geometry in its definition of parallel lines. János Bolyai – Background Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai. Farkas…
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mathematics
Eugenio Beltrami and the Consistency of Non-Euclidian Geometry

Eugenio Beltrami and the Consistency of Non-Euclidian Geometry

Harald Sack
On November 16, 1835, Italian mathematician Eugenio Beltrami was born. He is most notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere. “Students should learn to study at an early stage the great works of the great masters instead of making their minds sterile through…
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