Minimaler Umkugelradius bei vierdimensionalen Simplexen mit Einschränkungen für ihre Kanten
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...
The Möbius metric is studied in the cases, where its domain is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains.
Using the geometry of the projective plane over the finite field , we construct a Hermitian Lorentzian lattice of dimension defined over a certain number ring that depends on . We show that infinitely many of these lattices are -modular, that is, , where is some prime in such that .The Lorentzian lattices sometimes lead to construction of interesting positive definite lattices. In particular, if is a rational prime such that is norm of some element in , then we find a dimensional...