Mappings preserving regular hexahedrons.
Many programs for the hidden lines on a surface are known [1] but these programs are long and need a large memory of the computer. In this paper we show algorithms and the corresponding mini-program in BASIC which can be implemented on minicomputers with plotters or plotting displays. We map the surface in the parallel or central projections.
We show that any convex Jordan curve in a normed plane admits an inscribed Minkowskian square. In addition we prove that no two different Minkowskian rhombi with the same direction of one diagonal can be inscribed in the same strictly convex Jordan curve.
Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball of a Euclidean 2-space is presented. This decomplexification proves useful, enabling the resulting...