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One configurational characterization of Ostrom nets

Jaromír Baštinec (1991)

Mathematica Bohemica

Bz the quadrileteral condition in a given net there is meant the following implication: If A 1 , A 2 , A 3 , A - 4 are arbitrary points, no three of them lie on the same line, with coll ( A i A j ) (collinearity) for any five from six couples { i , j } then there follows the collinearity coll ( A k A l ) for the remaining couple { k , l } . In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration...

Several observations about Maneeals - a peculiar system of lines

Naga Vijay Krishna Dasari, Jakub Kabat (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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|. A C n A B n = C D n B D n , A B n B C n = A E n C E n , B C n A C n = 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.

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