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Mathematical Treasure: Lobachevski's New Geometries

Frank J. Swetz (Pennsylvania State University)

This portrait of Nikolai Lobachevski (1792-1856), a founder of non-Euclidean geometry, appeared as a frontispiece for the 1914 English edition of his book Geometric Researches on the Theory of Parallels.

Geometric Researches on the Theory of Parallels (1914) was the first popular English language translation of Lobachevski’s work. Nikolai Lobachevski, a Russian mathematician and geometer, formulated a new geometry resulting from an alternate, non-Euclidean interpretation of parallelism. Although his revolutionary discoveries eventually earned him the title “the Copernicus of geometry,” they at first remained relatively unknown outside of Russia, where they were first published. They were translated into German and published in Europe in 1840. In 1891, George Halsted translated Lobachevski’s work from German to English, and published his translation in the Bulletin of the University of Texas at Austin to a limited audience. Finally, in 1914, Carus Publications published Halsted's English translation of Lobachevski’s Geometric Researches on the Theory of Parallels.

A discussion of the theory of parallel lines

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Lobachevski's New Geometries," Loci (October 2013)