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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 dimension of a special series can never exceed half its order.

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} is complete, even if one is restricted to subsequences in which no two consecutive ...

Almost all natural numbers are very, very, very large (Steinbach 1990, p. 111).

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...