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Let M be a compact n-dimensional manifold with injectivity radius inj(M). Then Vol(M)>=(c_ninj(M))/pi, with equality iff M is isometric to the standard round sphere S^n with ...

A graph with graph edges of two possible "colors," usually identified as red and blue. For a bichromatic graph with R red graph edges and B blue graph edges, R+B>=2.

If two complementary Plücker characteristics are equal, then each characteristic is equal to its complement except in four cases where the sum of order and class is 9.

A clear-cut way of describing every object in a class in a one-to-one manner.

The Chebyshev integral is given by intx^p(1-x)^qdx=B(x;1+p,1+q), where B(x;a,b) is an incomplete beta function.

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.

A geometric figure which touches only the vertices (or other extremities) of another figure.

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

The 6-polyiamond illustrated above.