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Johnson solid J_(48).

Two numbers are homogeneous if they have identical prime factors. An example of a homogeneous pair is (6, 72), both of which share prime factors 2 and 3: 6 = 2·3 (1) 72 = ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Rosenbrock methods.

The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is A=1/2nR^2sin((2pi)/n)=3.

Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...

The nth partial numerator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) is the expression a_n. For a simple continued fraction b_0+K_(n=1)^infty1/(b_n), ...

Let x:p(x)->xp(x), then for any operator T, T^'=Tx-xT is called the Pincherle derivative of T. If T is a shift-invariant operator, then its Pincherle derivative is also a ...

The derivative rule d/(dx)[(f(x))/(g(x))]=(g(x)f^'(x)-f(x)g^'(x))/([g(x)]^2).

If f(x)=f_0+f_1x+f_2x^2+...+f_nx^n+..., (1) then S(n,j)=f_jx^j+f_(j+n)x^(j+n)+f_(j+2n)x^(j+2n)+... (2) is given by S(n,j)=1/nsum_(t=0)^(n-1)w^(-jt)f(w^tx), (3) where ...

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...