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A cube can be divided into n subcubes for only n=1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, and n>=48 (OEIS A014544; Hadwiger 1946; Scott 1947; Gardner 1992, ...

An l_x table is a tabulation of numbers which is used to calculate life expectancies. x n_x d_x l_x q_x L_x T_x e_x 0 1000 200 1.00 0.20 0.90 2.70 2.70 1 800 100 0.80 0.12 ...

Let F(n,sigma) denote the number of permutations on the symmetric group S_n which avoid sigma in S_k as a subpattern, where "tau contains sigma as a subpattern" is ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

A polynomial given by Phi_n(x)=product_(k=1)^n^'(x-zeta_k), (1) where zeta_k are the roots of unity in C given by zeta_k=e^(2piik/n) (2) and k runs over integers relatively ...

The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...