Fano plane

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English

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Fano plane

A diagram of the finite projective plane $\mathbb {P} ^{2}(\mathbb {F} _{2})$ , a.k.a. Fano plane. (In this presentation of it, the labels are vectors over the finite field $\mathbb {F} _{2}$ ; 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 $\mathbb {F} _{2}^{2}$ .)

Etymology

Named after Gino Fano (1871–1952), an Italian mathematician.

Noun

Fano plane (plural Fano planes)

(geometry) 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.

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