Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T01:34:11.998Z Has data issue: false hasContentIssue false

A Generalization of the Pappus Configuration

Published online by Cambridge University Press:  20 November 2018

Gerald Berman*
Affiliation:
Illinois Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A configuration is a system of m points and n lines such that each point lies on μ of the lines and each line contains v of the points. It is usually denoted by the symbol (mμ,nμ) with = nv. Two configurations corresponding to the same symbol are said to be equivalent if there exist 1-1 mappings of the points and lines of one onto the points and lines of the other which preserve the incidence relations.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1951

References

[1] Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc,vol. 56 (1950), 413455.Google Scholar
[2] Feld, J. M., Configurations inscriptible in a plane cubic curve, Amer. Math. Monthly, vol. 43 (1936), 549555.Google Scholar
[3] Hesse, O., Über Curven dritter Ordnung und die Kegelschnitte welche diese Curven in drei verschiedenen Punkten beruhren, J. Reine Angew. Math., vol. 36 (1848), 143176.Google Scholar
[4] Reye, Th., Das Problem der Configurationen, Acta Math., vol. 1 (1882), 97108.Google Scholar
[5] Zacharias, M., Untersuchungen uber ebene Konfigurationen (124, 163), Deutsche Math,vol. 6 (1941), 147170.Google Scholar
[6] Zacharias, M., Eine ebene Konfiguration (124, 163) in der Dreiecksgeometrie, Monatsh. Math. Phys., vol. 44 (1936), 153158.Google Scholar
[7] Zacharias, M., Über den Zusammenhang des Morleyschen Satzes von den winkeldrittelnden Eckenlinienen eines Dreiecks mit den trilinearen Verwandtschaften in Dreieck und mit einer Konfiguration (124, 163) der Dreiecksgeometrie, Deutsche Math., vol. 3 (1938), 3645.Google Scholar