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Monge configurations and their extensions

Guzowski A.

Zeszyty Naukowe. Geometria / Politechnika Poznańska

2002

Nr XXII

17-38

In this work we are engaged with one of typical configurations appearing in descriptive geometry, more exactly with the configuration which can be seen drawing Monge projections of a pair of crossing lines. In the first section we define Monge configuration. In the second section we characterize the group of collineations of Monge configuration. We find its correlations and characterize the configuration in terms of ranks of points and lines. The third section is devoted to considerations on axioms associated with Monge configurations. There are two main theorems of this chapter. The first is Theorem 4.5. In descriptive geometry all configuration axioms associated with Monge configurations are mutually equivalent. The second is Theorem 4.7: Monge axiom is a consequence of Desargue's axiom, so Monge configurations have to close on Desarguesian planes. In the last section we study special Monge configurations, i.e. configurations in which besides incidences characteristic for Monge configurations, there occur some additional. Main results of this section state conditions which must satisfy a protective plane containing such a configuration.