Prove that a finite projective plane of order n has n2 + n + 1 points and n2 + n + 1 lines.
Prove that a finite projective plane of order n has n2 + n + 1 points and n2 + n + 1 lines.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove that a finite projective plane of order n has n2 + n + 1 points and
n2 + n + 1 lines.
Expert Solution
Step 1
Let p be an ambitrany point, each point in it determinis a line together with P which Obviously passes Through P. Hence, all the points of it Lie on nty lines incient with P. Each of these lines incident with points other then P. So there and n(n+1) of them are including P.We get (n^2+n+1)Points on it..
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