Search Results for ""

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...

The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.

A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

An axiomatic theory (such as a geometry) is said to be complete if each valid statement in the theory is capable of being proven true or false.

The five of Hilbert's axioms which concern geometric equivalence.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

A fractal curve of infinite length which bounds an area twice that of the original square.

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...