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Let DeltaA^'B^'C^' be a triangle perspective to a reference triangle DeltaABC with perspector D^(''). Let A^('') be the intersection of lines BC^' and CB^', B^('') the ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...

A prime p_n is called "good" if p_n^2>p_(n-i)p_(n+i) for all 1<=i<=n-1 (there is a typo in Guy 1994 in which the is are replaced by 1s). There are infinitely many good ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...

The case of the Weierstrass elliptic function with invariants g_2=1 and g_3=0. In this case, the half-periods are given by (omega_1,omega_2)=(omega,iomega), where omega is ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...