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Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

In the equianharmonic case of the Weierstrass elliptic function, corresponding to invariants g_2=0 and g_3=1, the corresponding real half-period is given by omega_2 = ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

Define the harmonic mean of the divisors of n H(n)=(sigma_0(n))/(sum_(d|n)1/d), where sigma_0(n) is the divisor function (the number of divisors of n). For n=1, 2, ..., the ...

The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in ...

If P(z) is a power series which is regular for |z|<=1 except for m poles within this circle and except for z=+1, at which points the function is assumed continuous when only ...

The theory of natural numbers defined by the five Peano's axioms. Paris and Harrington (1977) gave the first "natural" example of a statement which is true for the integers ...

A skewed distribution which is similar to the binomial distribution when p!=q (Abramowitz and Stegun 1972, p. 930). y=k(t+A)^(A^2-1)e^(-At), (1) for t in [0,infty) where A = ...

The pentakis dodecahedron is the 60-faced dual polyhedron of the truncated icosahedron A_(11) (Holden 1971, p. 55). It is Wenninger dual W_9. It can be constructed by ...