2D, 3D, and 4D Geometric Algebras

Eduardo Bayro-Corrochano ()
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Eduardo Bayro-Corrochano: CINVESTAV, Electrical Engineering and Computer Science Department

Chapter Chapter 4 in Geometric Algebra Applications Vol. II, 2020, pp 125-152 from Springer

Abstract: Abstract It is the belief that imaginary numbers appeared for the first time around 1540 when the mathematicians Tartaglia and Cardano represented real roots of a cubic equation in terms of conjugated complex numbers. A Norwegian surveyor, Caspar Wessel, was in 1798 the first one to represent complex numbers by points on a plane with its vertical axis imaginary and horizontal axis real. This diagram was later known as the Argand diagram, although the true Aragand’s achievement was an interpretation of $$i=\sqrt{({-}1)}$$ as a rotation by a right angle in the plane. Complex numbers received their name by Gauss, and their formal definition as pair of real numbers was introduced by Hamilton in 1835.

Date: 2020
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DOI: 10.1007/978-3-030-34978-3_4

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