The Fano Plane

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# The Fano Plane - PowerPoint PPT Presentation

The Fano Plane. By Ed Pegg Jr mathpuzzle.com maa.org Math Games mathworld.com. The Fano Plane. “I have a Fano Plane.”. The Fano Plane. The {1,2,4} Switching Network. The Fano Plane. The Heawood Graph – a {3,6} cage. The Fano Plane. Heawood as attacking Queens – Geoff Exoo.

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Presentation Transcript
The Fano Plane

By Ed Pegg Jr

mathpuzzle.com

maa.org Math Games

mathworld.com

The Fano Plane

“I have a Fano Plane.”

The Fano Plane

The {1,2,4} Switching Network

The Fano Plane

The Heawood Graph – a {3,6} cage

The Fano Plane

Heawood as attacking Queens – Geoff Exoo

The Fano Plane

The Seven coloring of the Torus

(done with dominoes, just for the challenge)

The Fano Plane

The Szilassi Polyhedron

A seven-coloring of the torus

The Fano Plane

A seven-coloring of the torus

18 different heptominoes (Roger Phillips)

The Fano Plane

As an error correcting code

(The Inquisitive Problem Solver)

The Fano Plane

Corners of a die (+7, if odd)

Opposing faces of a die (+7, if odd)

Winning positions in Nim heaps less than 8 (Conway, Roller – The Inquisitive Problem Solver)

The Fano Plane

Fire and Ice (a fano plane of fano planes)

(Jens-Peter Schliemann)

The Fano Plane

The multiplication of octonions

(John Baez)

The Fano Plane

Can you hear the shape of a drum?

(Olivier Giraud - http://arxiv.org/abs/nlin.CD/0503069)

The Fano Plane

Another visualization of the Fano plane

(Burkard Polster)

The Fano Plane

The smallest Projective Space

http://homepages.wmich.edu/~drichter/projectivespace.htm

http://www.maths.monash.edu.au/~bpolster/perfect.html

The Fano Plane

The Hoffman-Singleton Graph

The Fano Plane

The Hoffman-Singleton Graph

as a deck of 50 cards.

The Fano Plane

The Hoffman-Singleton Graph

as a deck of 50 cards.