Geometry and Trigonometry

Other Geometries

Who further developed the ideas in non-Euclidean geometry?

In 1854, German mathematician Georg Friedrich Bernhard Riemann (1826–1866) presented several new general geometric principles, laying the foundations of a non-Euclidean system of geometry called elliptical or Riemann geometry. In this, he represented elliptic space and generalized the work of German mathematician Karl Friedrich Gauss in differential geometry. Riemann’s studies would eventually provide the basic tools for the general theory of relativity’s mathematical expression. For example, the type of non-Euclidian geometry suggested by Riemann enabled Albert Einstein (1897–1955) to work on his general relativity theory (1916), showing that the true geometry of space may be non-Euclidian. (For more about Riemann, see “Math Basics.”)


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