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Discrete Laplace cycles of period four

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Schröcker H.-P.

Open Mathematics

2012

tom 10

nr 2

426-439

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.

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Several observations about Maneeals - a peculiar system of lines

100%

Dasari N. V. K., Kabat J.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2016

tom 15

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|. $$\matrix{{{{\left| {AC} \right|^n } \over {\left| {AB} \right|^n }} = {{\left| {CD_n } \right|} \over {\left| {BD_n } \right|}},} \hfill & {{{\left| {AB} \right|^n } \over {\left| {BC} \right|^n }} = {{\left| {AE_n } \right|} \over {\left| {CE_n } \right|}},} \hfill & {{{\left| {BC} \right|^n } \over {\left| {AC} \right|^n }} = {{\left| {BF_n } \right|} \over {\left| {AF_n } \right|}}.}} $$ 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.

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

1 Open Mathematics

1 Dasari N. V. K.

1 Kabat J.

1 Schröcker H.-P.

1 2016

1 2012

Wyniki wyszukiwania

Discrete Laplace cycles of period four

Several observations about Maneeals - a peculiar system of lines