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The Bolyai expansion of a real number x is a nested root of the form x=a_0-1+RadicalBox[{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m], ...

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 repeated application of a transformation.

The mixtilinear circle is the circumcircle of the mixtilinear triangle, i.e., the triangle formed by the centers of the mixtilinear incircles. Neither its center not circle ...

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 ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

Given a number z, the cube root of z, denoted RadicalBox[z, 3] or z^(1/3) (z to the 1/3 power), is a number a such that a^3=z. The cube root is therefore an nth root with ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...