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Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

van der Waerden's theorem is a theorem about the existence of arithmetic progressions in sets. The theorem can be stated in four equivalent forms. 1. If N=C_1 union C_2 union ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

Let {f_n} and {a_n} be sequences with f_n>=f_(n+1)>0 for n=1, 2, ..., then |sum_(n=1)^ma_nf_n|<=Af_1, where A=max{|a_1|,|a_1+a_2|,...,|a_1+a_2+...+a_m|}.

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in ...

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.