Several observations about Maneeals - a peculiar system of lines

Naga Vijay Krishna Dasari; Jakub Kabat

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 15 (2016), / Harvested from The Polish Digital Mathematics Library

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Résumé

For an arbitrary triangle ABC and an integer n we define points Dn, En, Fn on the sides BC, CA, AB respectively, in such a manner that |AC|n|AB|n=|CDn||BDn|,|AB|n|BC|n=|AEn||CEn|,|BC|n|AC|n=|BFn||AFn|. $\frac{{|A C|}^{n}}{{|A B|}^{n}} = \frac{|C D_{n}|}{|B D_{n}|}, \frac{{|A B|}^{n}}{{|B C|}^{n}} = \frac{|A E_{n}|}{|C E_{n}|}, \frac{{|B C|}^{n}}{{|A C|}^{n}} = \frac{|B F_{n}|}{|A F_{n}|} .$ Cevians ADn, BEn, CFn are said to be the Maneeals of order n. In this paper we discuss some properties of the Maneeals and related objects.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:287139

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     author = {Naga Vijay Krishna Dasari and Jakub Kabat},
     title = {Several observations about Maneeals - a peculiar system of lines},
     journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
     volume = {15},
     year = {2016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2016-0005}
}

Naga Vijay Krishna Dasari; Jakub Kabat. Several observations about Maneeals - a peculiar system of lines. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 15 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2016-0005/