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New Algebraic Tools for Classical Geometry

  • David Hestenes
  • Hongbo Li
  • Alyn Rockwood
Chapter

Abstract

Classical geometry has emerged from efforts to codify perception of space and motion. With roots in ancient times, the great flowering of classical geometry was in the 19th century, when Euclidean, non-Euclidean and projective geometries were given precise mathematical formulations and the rich properties of geometric objects were explored. Though fundamental ideas of classical geometry are permanently imbedded and broadly applied in mathematics and physics, the subject itself has practically disappeared from the modern mathematics curriculum. Many of its results have been consigned to the seldom-visited museum of mathematics history, in part, because they are expressed in splintered and arcane language. To make them readily accessible and useful, they need to be reexamined and integrated into a coherent mathematical system.

Keywords

Geometric Object Orthogonal Transformation Geometric Algebra Dual Frame Outer Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • David Hestenes
    • 1
  • Hongbo Li
    • 1
  • Alyn Rockwood
    • 2
  1. 1.Department of Physics and AstronomyArizona State UniversityTempeUSA
  2. 2.Power Take Off Software, Inc.Colorado SpringsUSA

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