The Fano plane is a finite projective plane with the smallest possible number of points and lines: seven points and seven lines, arranged so that every line contains exactly three points and every point lies on exactly three lines. It is named for the Italian mathematician Gino Fano, an early investigator of finite projective geometries. The plane can be constructed from the two-element finite field, and is formally denoted PG(2, 2); its combination of minimal size and perfect symmetry makes it a standard first example in finite geometry and a recurring structure in combinatorial design theory and coding theory.
Facts
FAQs
Can the Fano plane be drawn with straight lines in the ordinary plane?
No. It is not realizable over the real or rational numbers.
No. The Fano plane is the two-dimensional finite projective plane over the Galois field of order 2, with seven points and seven lines, and Wolfram MathWorld notes that it is not realizable over the real or rational numbers. That means no arrangement of seven points and seven straight lines in the ordinary real plane reproduces its incidence structure exactly.
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Sources
1. Fano Plane (Wikipedia)
Wikimedia FoundationLead section
In finite geometry, the Fano plane (named after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point.
- In Branch: Discrete Geometry
View the Source 2. Gino Fano (1871-1952), Biography, MacTutor History of Mathematics
Biography, list of publicationsQuote, Biography, list of publications
Fano wrote in his 1892 paper Sui postulati fondamentali della geometria in uno spazio lineare ad un numero qualunque di dimensioni
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