Definition:Fano Plane
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Definition
The Fano plane is the finite projective plane of order $2$.
It can be denoted:
- $\operatorname {PG} \left({2, 2}\right)$
where:
- $\operatorname {PG}$ stands for projective geometry
- the first parameter $2$ specifies the dimension
- the second parameter $2$ specifies the order.
$\operatorname {PG} \left({2, 2}\right)$ has the following properties:
- It has $7$ points
- It has $7$ lines
- There are $3$ points on each line
- There are $3$ lines through each point.
Also see
From Structure of Fano Plane, $\operatorname {PG} \left({2, 2}\right)$ has the fewest points and lines.
Source of Name
This entry was named for Gino Fano.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $7$
- Weisstein, Eric W. "Fano Plane." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FanoPlane.html