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Mini-programs for hidden lines on a surface

Josef Kateřiňák (1987)

Aplikace matematiky

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.

Minkowskian rhombi and squares inscribed in convex Jordan curves

Horst Martini, Senlin Wu (2010)

Colloquium Mathematicae

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.

Möbius gyrovector spaces in quantum information and computation

Abraham A. Ungar (2008)

Commentationes Mathematicae Universitatis Carolinae

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 𝔹 2 of a Euclidean 2-space 2 is presented. This decomplexification proves useful, enabling the resulting...

Möbius metric in sector domains

Oona Rainio, Matti Vuorinen (2023)

Czechoslovak Mathematical Journal

The Möbius metric δ G is studied in the cases, where its domain G 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.

Modular lattices from finite projective planes

Tathagata Basak (2014)

Journal de Théorie des Nombres de Bordeaux

Using the geometry of the projective plane over the finite field 𝔽 q , we construct a Hermitian Lorentzian lattice L q of dimension ( q 2 + q + 2 ) defined over a certain number ring 𝒪 that depends on q . We show that infinitely many of these lattices are p -modular, that is, p L q ' = L q , where p is some prime in 𝒪 such that | p | 2 = q .The Lorentzian lattices L q sometimes lead to construction of interesting positive definite lattices. In particular, if q 3 mod 4 is a rational prime such that ( q 2 + q + 1 ) is norm of some element in [ - q ] , then we find a 2 q ( q + 1 ) dimensional...

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