INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(3221)
(SS(a->bc) OF X(647))


Click here to access the list of all triangle centers.

Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(b2 - c2)(c2a2 + a2b2 - b2c2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

Trilinears for X(3221) are obtained by applying the symbolic substitution (a,b,c)-->(bc,ca,ab) to trilinear coordinates of X(647). As a symbolic substitution, this mapping takes lines onto lines. In particular, points on the Euler line, X(2)X(3), with coefficients given by X(647), are mapped to the line X(6)X(194), with coefficients given by X(3221). Symbolic substitutions are introduced in the following article:

C. Kimberling, "Symbolic substitutions in the transfigured plane of a triangle," Aequationes Mathematicae 73 (2007) 156-171.

X(3221) lies on these lines: 30,511    669,2451    882,1843

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense



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