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The common incircle of the medial triangle DeltaM_AM_BM_C (left figure) and the congruent triangle DeltaQ_AQ_BQ_C, where Q_i are the midpoints of the line segment joining the ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

Convergents of the pi continued fractions are the simplest approximants to pi. The first few are given by 3, 22/7, 333/106, 355/113, 103993/33102, 104348/33215, ... (OEIS ...

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that x in muB for all mu in F with |mu|>=lambda, where F is the ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

For real, nonnegative terms x_n and real p with 0<p<1, the expression lim_(k->infty)x_0+(x_1+(x_2+(...+(x_k)^p)^p)^p)^p converges iff (x_n)^(p^n) is bounded.

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...