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Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. According to Wolfram (2002, p. 860), logic is the most ...

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, ...

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

There are six Painlevé transcendents, corresponding to second-order ordinary differential equations whose only movable singularities are ordinary poles and which cannot be ...

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

The rhombic dodecahedral graph is the Archimedean dual graph which is the skeleton of the rhombic dodecahedron (as well as the Bilinski dodecahedron). It is the Levi graph of ...