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Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

The center of an inner Soddy circle. It has equivalent triangle center functions alpha = 1+(2Delta)/(a(b+c-a)) (1) alpha = sec(1/2A)cos(1/2B)cos(1/2C)+1, (2) where Delta is ...

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

(1) for p in [0,1], where delta is the central difference and E_(2n) = G_(2n)-G_(2n+1) (2) = B_(2n)-B_(2n+1) (3) F_(2n) = G_(2n+1) (4) = B_(2n)+B_(2n+1), (5) where G_k are ...

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

The Heilbronn triangle problem is to place n>=3 points in a disk (square, equilateral triangle, etc.) of unit area so as to maximize the area Delta(n) of the smallest of the ...