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A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

A zonohedron which is the dual of the dodecadodecahedron U_(36) and Wenninger dual W_(73). The medial rhombic triacontahedron contains interior pentagrammic vertices which ...

A modification of Legendre's formula for the prime counting function pi(x). It starts with |_x_| = (1) where |_x_| is the floor function, P_2(x,a) is the number of integers ...

Minesweeper is single-player logic-based computer game played on rectangular board whose object is to locate a predetermined number of randomly-placed "mines" in the shortest ...

In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language). The ...

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive ...