Search Results for ""

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

Barycentric coordinates are triples of numbers (t_1,t_2,t_3) corresponding to masses placed at the vertices of a reference triangle DeltaA_1A_2A_3. These masses then ...

A chordless cycle of a graph G is a graph cycle in G that has no cycle chord. Unfortunately, there are conflicting conventions on whether or not 3-cycles should be considered ...

For s>1, the Riemann zeta function is given by zeta(s) = sum_(n=1)^(infty)1/(n^s) (1) = product_(k=1)^(infty)1/(1-1/(p_k^s)), (2) where p_k is the kth prime. This is Euler's ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...