**Partial Geometries**

One can construct partial geometries, derived from maximal arcs:

- Let
*K*be a maximal arc with degree*d*. Consider the incidence structure, where P contains all points of the projective plane not on*K*, B contains all line of the projective plane intersecting*K*in*d*points, and the incidence*I*is the natural inclusion. This is a partial geometry : . - Consider the space and let
*K*a maximal arc of degree in a two-dimensional subspace . Consider an incidence structure where*P*contains all the points not in,*B*contains all lines not in and intersecting in a point in*K*, and*I*is again the natural inclusion. is again a partial geometry : .

Read more about this topic: Maximal Arc

### Famous quotes containing the word partial:

“America is hard to see.

Less *partial* witnesses than he

In book on book have testified

They could not see it from outside....”

—Robert Frost (1874–1963)

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