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:
“Being blunt with your feelings is very American. In this big country, I can be as brash as New York, as hedonistic as Los Angeles, as sensuous as San Francisco, as brainy as Boston, as proper as Philadelphia, as brawny as Chicago, as warm as Palm Springs, as friendly as my adopted home town of Dallas, Fort Worth, and as peaceful as the inland waterway that rubs up against my former home in Virginia Beach.”
—Martina Navratilova (b. 1956)
“A poet is no rattlebrain, saying what comes uppermost, and, because he says every thing, saying, at last, something good; but a heart in unison with his time and country. There is nothing whimsical or fantastic in his production, but sweet and sad earnest, freighted with the weightiest convictions, and pointed with the most determined aim which any man or class knows of in his times.”
—Ralph Waldo Emerson (1803–1882)
“...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)