Other Properties
A set of five or more points is concyclic if and only if every four-point subset is concyclic. This property can be thought of as an analogue for concyclicity of the Helly property of convex sets.
Abouabdillah's theorem characterizes the similarity transformations of a Euclidean space of dimension two or more as being the only surjective mappings of the space to itself that preserve concyclicity.
Read more about this topic: Concyclic Points
Famous quotes containing the word properties:
“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 (1803–1882)
“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 (1632–1704)