Trigonometry in the Minkowski Plane

Part of the Frontiers in Mathematics book series (FM)


We have seen in Section 3.2 how commutative hypercomplex numbers can be associated with a geometry, in particular the two-dimensional numbers can represent the Euclidean plane geometry and the space-time (Minkowski) plane geometry. In this chapter, by means of algebraic properties of hyperbolic numbers, we formalize the space-time geometry and trigonometry. This formalization allows us to work in Minkowski space-time as we usually do in the Euclidean plane, i.e., to give a Euclidean description that can be considered similar to Euclidean representations of non-Euclidean geometries obtained in the XIXth century by E. Beltrami [2] on constant curvature surfaces, as we recall in Chapter 9.


Lorentz Transformation Euclidean Plane Hyperbolic Plane Minkowski Plane Hyperbolic Number 
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© Birkhäuser Verlag AG 2008

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