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Fano plane
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Fano plane
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A diagram of the finite projective plane
P
2
(
F
2
)
{\displaystyle \mathbb {P} ^{2}(\mathbb {F} _{2})}
, a.k.a. Fano plane. (In this presentation of it, the labels are vectors over the finite field
F
2
{\displaystyle \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
F
2
2
{\displaystyle \mathbb {F} _{2}^{2}}
.)
Etymology
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Named after
Gino Fano
(1871–1952), an Italian mathematician.
Noun
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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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en:Geometry
en:Manifolds
en:Surfaces
en:Seven
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