From the early 1800s Gauss had an interest in the question of the possible existence of a non-Euclidean geometry.
non-Euclidean space, as his framework.
non-Euclidean space metrics.
The most significant discoveries of KSU include non-Euclidean geometry, obtaining aniline from nitrobenzene, new element ruthenium, phenomenon of EPR.
other words, by a non-Euclidean construction he trisected the angle AOC, for it is readily seen that, since FD' = FO = OC, the angle FOB = 2 AOC. 6 This couplet of constructions is as important from the calculator's point of view as it is interesting geometrically.
The most significant discoveries of KSU include non-Euclidean geometry, obtaining aniline from nitrobenzene, new element Ruthenium, phenomenon of EPR.
Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.
A special application of his theory of continuous groups was to the general problem of non-Euclidean geometry.
0) 2 = i suitable for non-Euclidean space, and w 2 = o suitable for Euclidean space; we confine ourselves to the second, and will call the indicated bi-quaternion p+wq an octonion.
He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers "Preliminary Sketch of Bi-quaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.
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