Erlangen Program at Large--2: Inventing a wheel. The parabolic one

Details Erlangen Program at Large--2: Inventing a wheel. The parabolic one Erlangen Program at Large--2: Inventing a wheel. The parabolic one

2007-07-27

arxiv.org/abs/0707.4024v1

Trans. Inst. Math. of the NAS of Ukraine, v. 7, n. 2, pp. 89--98, 2010

Mathematics

General Mathematics

LaTeX paper (14 pages) and software documentation in an appendix (20 pages); two figures (five PS files)

Scientific paper

We discuss parabolic versions of Euler's identity e^{it}=cos t + i sin t. A purely algebraic approach based on dual numbers is known to produce a very trivial relation e^{pt} = 1+pt. Therefore we use a geometric setup of parabolic rotations to recover the corresponding non-trivial algebraic framework. Our main tool is Moebius transformations which turn out to be closely related to induced representations of the group SL(2,R). Keywords: complex numbers, dual numbers, double numbers, linear algebra, invariant, computer algebra, GiNaC

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