Abstract
In this chapter vectors are introduced into hyperbolic geometry, where they are called gyrovectors. Gyrovectors are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrangle the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrangle the two diagonals of which intersect at their midpoints.
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References
Ungar, A.A.: Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity, p. 628. World Scientific, Hackensack (2008)
Ungar, A.A.: A Gyrovector Space Approach to Hyperbolic Geometry. Morgan & Claypool, San Rafael (2009)
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Ungar, A.A. (2010). Gyrovectors. In: Hyperbolic Triangle Centers. Fundamental Theories of Physics, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8637-2_5
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DOI: https://doi.org/10.1007/978-90-481-8637-2_5
Publisher Name: Springer, Dordrecht
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