- The number of lines through a fixed point p, not on a maximal arc K, intersecting K in d points, equals . Thus, d divides q.
- In the special case of d = 2, maximal arcs are known as hyperovals which can only exist if q is even.
- An arc K having one fewer point than a maximal arc can always be uniquely extended to a maximal arc by adding to K the point at which all the lines meeting K in d - 1 points meet.
- In PG(2,q) with q odd, no non-trivial maximal arcs exist.
- In PG(2,2h), maximal arcs for every degree 2t, 1 ≤ t ≤ h exist.
Read more about this topic: Maximal Arc
Other articles related to "properties":
... Many of the Kiawah Island properties are located directly on the beach or just a short distance away, and there are numerous golf course properties and lagoon view properties as well ...
0.4 0.05 0.003 0.002 0.001 0.02 0.001 0.02 0.0005 0.001 Zamak 4 properties Property Metric value English value Mechanical properties Ultimate tensile strength 317 MPa 46,000 psi Yield strength (0.2% offset) 221 ...
... Further information Mineral physics The physical properties of minerals must be understood to infer the composition of the Earth's interior from ... Mineral physicists study the elastic properties of minerals their high-pressure phase diagrams, melting points and equations of state at high ... a very complex substance and its unique properties are essential for life ...
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (16321704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (18031882)