Consider an incidence geometry in which every line has at least three distinct points (rather than at least two as requiblack by the second axiom of Incidence Geometry). What are the least number of points and lines that must exist? Note: You can show the existence of such a "minimum" geometry by constructing a model for it. On the other hand, you have to prove that there cannot be a model with less points or lines

anudoneddbv 2022-07-27 Answered
Consider an incidence geometry in which every line has at least three distinct points (rather than at least two as requiblack by the second axiom of Incidence Geometry). What are the least number of points and lines that must exist? Note: You can show the existence of such a "minimum" geometry by constructing a model for it. On the other hand, you have to prove that there cannot be a model with less points or lines
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Answers (1)

Brendon Bentley
Answered 2022-07-28 Author has 11 answers
As per the new incidence rules, at least three points lie on a given line. For drawing two lines there has to be at least 5 lines. Thus a minimum of 5 points and two lines should exist.
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