Blunt and Pointed Cones
According to the above definition, if C is a convex cone, then C{0} is a convex cone, too. A convex cone is said to be pointed or blunt depending on whether it includes the null vector 0 or not. Blunt cones can be excluded from the definition of convex cone by substituting "non-negative" for "positive" in the condition of α, β. The term "pointed" is also often used to refer to a closed cone that contains no complete line (i.e., no nontrivial subspace of the ambient vector space V), i.e. what is called a "salient" cone below.
Read more about this topic: Convex Cone
Famous quotes containing the words blunt, pointed and/or cones:
“He sits, strong and blunt as a Celtic cross,
Clearly used to silence and an armchair:
Tonight the wife and children will be quiet
At slammed door and smoker’s cough in the hall.”
—Seamus Heaney (b. 1939)
“Be sure that it is not you that is mortal, but only your body. For that man whom your outward form reveals is not yourself; the spirit is the true self, not that physical figure which can be pointed out by your finger.”
—Marcus Tullius Cicero (106–43 B.C.)
“...there was the annual Fourth of July picketing at Independence Hall in Philadelphia. ...I thought it was ridiculous to have to go there in a skirt. But I did it anyway because it was something that might possibly have an effect. I remember walking around in my little white blouse and skirt and tourists standing there eating their ice cream cones and watching us like the zoo had opened.”
—Martha Shelley, U.S. author and social activist. As quoted in Making History, part 3, by Eric Marcus (1992)