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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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Question

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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