Fano plane

English

A diagram of the finite projective plane ${\mathbb{P}}^2({𝔽}_2)$, a.k.a. Fano plane. (In this presentation of it, the labels are vectors over the finite field ${𝔽}_2$; vectors on the same line are linearly dependent. Vectors whose third component is zero are “at infinity”, whereas the ones whose third component is one form a 2×2 array, suggestive of ${𝔽}_2^2$.)

Etymology

Named after Template:W (1871–1952), an Italian mathematician.

Noun

1. Template:Lb The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.