Geometric point-circle pentagonal geometries from Moore graphs
| Autor: | Klara Stokes, Milagros Izquierdo |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Algebra and Number Theory
Euclidean space Desargues configuration Geometry Hypersphere Theoretical Computer Science Combinatorics Real projective plane Seven circles theorem Five circles theorem Line (geometry) Discrete Mathematics and Combinatorics Point (geometry) Geometry and Topology Mathematics |
| Zdroj: | Ars mathematica contemporanea |
| ISSN: | 1855-3974 1855-3966 |
| Popis: | We construct isometric point-circle configurations on surfaces from uniform maps. This gives one geometric realisation in terms of points and circles of the Desargues configuration in the real projective plane, and three distinct geometric realisations of the pentagonal geometry with seven points on each line and seven lines through each point on three distinct dianalytic surfaces of genus 57. We also give a geometric realisation of the latter pentagonal geometry in terms of points and hyperspheres in 24 dimensional Euclidean space. From these, we also obtain geometric realisations in terms of points and circles (or hyperspheres) of pentagonal geometries with ?$k$? circles (hyperspheres) through each point and ?$k-1$? points on each circle (hypersphere). Konstruiramo izometrične konfiguracije točk in krožnic na ploskvah iz uniformnih zemljevidov. Tako dobimo geometrijsko realizacijo s točkami in krožnicami Desarguesove konfiguracije v realni projektivni ravnini, in tri različne geometrijske realizacije petkotniške simetrije s sedmimi točkami na vsaki premici in sedmimi premicami skozi vsako točko na treh različnih dianalitičnih ploskvah roda 57. Podamo tudi geometrijsko realizacijo te zadnje petkotniške geometrije s točkami in hipersferami v 24-dimenzionalnem Evklidskem prostoru. Od tod dobimo tudi geometrijske realizacije s točkami in krožnicami (ali hipersferami) petkotniških geometrij s ?$k$? krožnicami (hipersferami) skozi vsako točko in ?$k-1$? točkami na vsaki krožnici (hipersferi). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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