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In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe. The axis of a cone is the straight line passing through the apex about which the base (and the whole cone) has a circular symmetry.
A cone is a convex cone if + belongs to , for any positive scalars , , and any , in . [5] [6] A cone is convex if and only if +.This concept is meaningful for any vector space that allows the concept of "positive" scalar, such as spaces over the rational, algebraic, or (more commonly) the real numbers.
The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by
A Hertzian cone is the cone produced when an object passes through a solid, such as a bullet through glass. More technically, it is a cone of force that propagates through a brittle, amorphous, or cryptocrystalline solid material from a point of impact. This force eventually removes a full or partial cone in the material. [1]
More generally, given a vector bundle (finite-rank locally free sheaf) E on X, if R=Sym(E *) is the symmetric algebra generated by the dual of E, then the cone is the total space of E, often written just as E, and the projective cone is the projective bundle of E, which is written as ().
Rolling cone motion is the rolling motion generated by a cone rolling over another cone. In rolling cone motion, at least one of the cones is convex , while the other cone may be either convex, or concave, or a flat surface (a flat surface can be regarded as a special case of a cone whose apex angle equals π {\displaystyle \pi } ).
Not all questions have simple, yes or no answers—including this one. While many dogs are lactose intolerant, many are not! Lactose intolerance develops as a dog grows up, so it can be impossible ...
A vapor cone (also known as a Mach diamond, [1] shock collar, or shock egg) is a visible cloud of condensed water that can sometimes form around an object moving at high speed through moist air, such as an aircraft flying at transonic speeds. When the localized air pressure around the object drops, so does the air temperature.
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