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The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

The Mandart circle is the circumcircle of the extouch triangle. It has center at Kimberling center X_(1158), which has trilinear center function (1) and radius ...

(1) where H_n(x) is a Hermite polynomial (Watson 1933; Erdélyi 1938; Szegö 1975, p. 380). The generating function ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

The geometric centroid of the first Morley triangle, which is also the center of Morley's circle, is called the first Morley center. It has triangle center function ...

Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the step size). The function can then be fitted and evaluated at ...

A Saunders graphic is a plot of the dth base-b digits of a function f(x,y) as a function of x and y. The plots above show Saunders graphics for the functions ...

Let x be a positive number, and define lambda(d) = mu(d)[ln(x/d)]^2 (1) f(n) = sum_(d)lambda(d), (2) where the sum extends over the divisors d of n, and mu(n) is the Möbius ...