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The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Let three equal circles with centers J_A, J_B, and J_C intersect in a single point H and intersect pairwise in the points A, B, and C. Then the circumcircle O of the ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...

Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map x_(n+1)=2x_n (mod 1). (1) Then the number of periodic map orbits of period p ...

"Analysis of Variance." A statistical test for heterogeneity of means by analysis of group variances. ANOVA is implemented as ANOVA[data] in the Wolfram Language package ...