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A k-subset is a subset of a set on n elements containing exactly k elements. The number of k-subsets on n elements is therefore given by the binomial coefficient (n; k). For ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.

Although the inner shaded region has the same area as the outer shaded annulus, it appears to be larger. Since the rings are equally spaced, A_(inner) = pi·3^2=9pi (1) ...

Chrystal's identity is the algebraic identity ((b-c)^2+(b+c)^2+2(b^2-c^2))/((b^4-2b^2c^2+c^4)[1/((b-c)^2)+2/(b^2-c^2)+1/((b+c)^2)])=1 given as an exercise by Chrystal (1886).

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.

A coefficient of the Maclaurin series of 1/(ln(1+x))=1/x+1/2-1/(12)x+1/(24)x^2-(19)/(720)x^3+3/(160)x^4+... (OEIS A002206 and A002207), the multiplicative inverse of the ...

The nth-order Menger sponge graph is the connectivity graph of cubes in the nth iteration of the Menger sponge fractal. The first two iterations are shown above. The n-Menger ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...