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In finite geometry, the Fano plane (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.
- VII.2
- 7
- 2
- Desarguesian, Self-dual
6 days ago · Fano Plane. Download Wolfram Notebook. The Fano plane is the configuration consisting of the two-dimensional finite projective plane the Galois field of order 2 . It is not realizable over the real or rational numbers (Gropp 1997). The incidence structure of the Fano is plane illustrated above.
Oct 24, 2015 · Roots of Unity. A Few of My Favorite Spaces: The Fano Plane. The intuition-challenging Fano plane may be the smallest interesting configuration of points and lines. By Evelyn Lamb on...
The Fano plane is the projective plane over the 2-element field . In other words, it consists of lines through the origin in the vector space . Since every such line contains a single nonzero element, we can also think of the Fano plane as consisting of the seven nonzero elements of .
May 4, 2005 · Here is the usual model of the seven points and seven lines (including the circle) of the smallest finite projective plane (the Fano plane ): Fig. 2. Every permutation of the plane's points that preserves collinearity is a symmetry of the plane. The group of symmetries of the Fano plane is of order 168 and is isomorphic to the group PSL (2,7 ...
Jul 13, 2021 · The Fano plane is the most well-known finite projective plane (and also the smallest). Here is a drawing of it. It has \(7\) points and \(7\) lines, one of which is the circle around the middle.
The projective plane of order 2 is called the Fano plane. See also the article on finite geometry . Using the vector space construction with finite fields there exists a projective plane of order N = p n , for each prime power p n .
