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If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

The weak law of large numbers (cf. the strong law of large numbers) is a result in probability theory also known as Bernoulli's theorem. Let X_1, ..., X_n be a sequence of ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...