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

X(316)
(DROUSSENT PIVOT)


Click here to access the list of all triangle centers.

Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon Run Macro Tool, select the center name from the list and, then, click on the vertices A, B and C successively.

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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..


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) = bc(b4 + c4 - a4 - b2c2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b4 + c4 - a4 - b2c2

The reflection of X(99) in the polar of X(76).

Lucien Droussent, "Cubiques circulaires anallagmatiques par points réciproques ou isogonaux," Mathesis 62 (1953) 204-215.

X(316) lies on these lines:
2,187    4,69    15,303    16,302    30,99    115,385    148,538    183,381    249,297    265,290    298,530    299,531    376,1007    384,626    512,850    524,671    691,858

X(316) = midpoint of X(621) and X(622) X(316) = reflection of X(I) in X(J) for these (I,J): (15,624), (16,623), (99,325), (385,115), (691,858)
X(316) = isotomic conjugate of X(67)
X(316) = anticomplement of X(187)
X(316) = crosssum of X(39) and X(187)

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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