Finite Geometries, Codes, Latin Squares, and Other Pretty Creatures

Part of the Undergraduate Texts in Mathematics book series (UTM)


The Fano plane is a really small world (Figure 14.1). It only has 7 points, which form 7 lines. In the figure, 6 of these lines are straight and one is circular; but for the inhabitants of this tiny world (the Fanoans), the straight and curved lines look the same. Also, in our figure it seems that the circular line intersects some of the straight lines twice; but the intersection points that are not marked are not real intersection points, they are there only because we want to draw a picture of this very different world in our Euclidean plane.


Block Design Projective Plane Euclidean Plane Parity Check Affine Plane 
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Copyright information

© Springer Science+Business Media, LLC 2003

Authors and Affiliations

  1. 1.Microsoft ResearchMicrosoft CorporationRedmondUSA
  2. 2.Department of Algebra and Number TheoryEõtvõs Loránd UniversityBudapestHungary
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA

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