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If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

A base-b BBP-type formula is a convergent series formula of the type alpha=sum_(k=0)^infty(p(k))/(b^kq(k)) (1) where p(k) and q(k) are integer polynomials in k (Bailey 2000; ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

An accumulation point is a point which is the limit of a sequence, also called a limit point. For some maps, periodic orbits give way to chaotic ones beyond a point known as ...

Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere. ...

The property of being continuous.

Construct a 5×5×5 cube from thirteen 1×2×4 blocks, one 2×2×2 block, one 1×2×2, and three 1×1×3 blocks.

Two variates A and B are statistically independent iff the conditional probability P(A|B) of A given B satisfies P(A|B)=P(A), (1) in which case the probability of A and B is ...

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of ...