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:
“Give me the keys. I feel for the common chord again,
Sliding by semi-tones till I sink to a minor,—yes,
And I blunt it into a ninth, and I stand on alien ground,
Surveying a while the heights I rolled from into the deep;
Which, hark, I have dared and done, for my resting-place is found,
The C Major of this life: so, now I will try to sleep.”
—Robert Browning (1812–1889)
“If somebody says, “I love you,” to me, I feel as though I had a pistol pointed at my head. What can anybody reply under such conditions but that which the pistol-holder requires? “I love you, too.””
—Kurt Vonnegut, Jr. (b. 1922)
“...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)