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Dissect a triangle into smaller triangles, such that all have full edge contact with their neighbors. Label the corners 1, 2, and 3. Label all vertices with 1, 2, or 3, with ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. The most common type of vertex ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

A k-subset is a subset of a set on n elements containing exactly k elements. The number of k-subsets on n elements is therefore given by the binomial coefficient (n; k). For ...

By way of analogy with the eban numbers, uban numbers are defined as numbers whose English names do not contain the letter "u" (i.e., "u" is banned). Note that this ...

A sequence {nu_i} of nondecreasing positive integers is complete iff 1. nu_1=1. 2. For all k=2, 3, ..., s_(k-1)=nu_1+nu_2+...+nu_(k-1)>=nu_k-1. A corollary states that a ...

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...

E(a,b)/p denotes the elliptic group modulo p whose elements are 1 and infty together with the pairs of integers (x,y) with 0<=x,y<p satisfying y^2=x^3+ax+b (mod p) (1) with a ...