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In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...
David Orlin Hestenes (born May 21, 1933) is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, [1] and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.
Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley Classics series ( ISBN 0-471-60839-4 ). In 1962 Algèbre Géométrique , a translation into French by Michel Lazard , was published by Gauthier-Villars, and reprinted in 1996.
Like many of the others, it did this by teaching geometric transformations as a unifying approach between algebra and geometry. [ 15 ] Regardless of all these influences and other projects, the SSMCIS study group considered its work unique in scope and breadth, and Fehr wrote that "nowhere [else] had a total 7–12 unified mathematics program ...
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
98 Discrete Differential Geometry: Integrable Structure, Alexander I. Bobenko, Yuri B. Suris (2008, ISBN 978-0-8218-4700-8) 99 Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators, Gerald Teschl (2009, ISBN 978-0-8218-4660-5) [12] 100 Algebra: A Graduate Course, I. Martin Isaacs (1994, ISBN 978-0-8218-4799-2)
The first complete axiom system for geometry was given only at the end of the 19th century by David Hilbert. At the same time, it appeared that both synthetic methods and analytic methods can be used to build geometry. The fact that the two approaches are equivalent has been proved by Emil Artin in his book Geometric Algebra.
Some of his books are: Introduction to Topology and Modern Analysis (1963) [7] Differential Equations with Applications and Historical Notes (1972, 1991, 2016) [8] Precalculus Mathematics in a Nutshell (1981) [9] Calculus with Analytic Geometry (1985, 1996) [10] Calculus Gems: Brief Lives and Memorable Mathematics (1992) [11]