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:
“A multitude of causes unknown to former times are now acting with a combined force to blunt the discriminating powers of the mind, and unfitting it for all voluntary exertion to reduce it to a state of almost savage torpor.”
—William Wordsworth (1770–1850)
“Semantically, taste is rich and confusing, its etymology as odd and interesting as that of “style.” But while style—deriving from the stylus or pointed rod which Roman scribes used to make marks on wax tablets—suggests activity, taste is more passive.... Etymologically, the word we use derives from the Old French, meaning touch or feel, a sense that is preserved in the current Italian word for a keyboard, tastiera.”
—Stephen Bayley, British historian, art critic. “Taste: The Story of an Idea,” Taste: The Secret Meaning of Things, Random House (1991)
“...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)