Several observations about Maneeals - a peculiar system of lines

Naga Vijay Krishna Dasari, and Jakub Kabat. "Several observations about Maneeals - a peculiar system of lines." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 15 (2016): 51-68. <http://eudml.org/doc/287139>.

@article{NagaVijayKrishnaDasari2016,
abstract = {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|. \[\{\{\{\{\left| \{AC\} \right|^n \} \over \{\left| \{AB\} \right|^n \}\} = \{\{\left| \{CD\_n \} \right|\} \over \{\left| \{BD\_n \} \right|\}\},\} \hfill & \{\{\{\left| \{AB\} \right|^n \} \over \{\left| \{BC\} \right|^n \}\} = \{\{\left| \{AE\_n \} \right|\} \over \{\left| \{CE\_n \} \right|\}\},\} \hfill & \{\{\{\left| \{BC\} \right|^n \} \over \{\left| \{AC\} \right|^n \}\} = \{\{\left| \{BF\_n \} \right|\} \over \{\left| \{AF\_n \} \right|\}\}.\}\} \] 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.},
author = {Naga Vijay Krishna Dasari, Jakub Kabat},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Maneeals; Maneeal’s Points; Maneeals triangle of order n; Maneeal’s Pedal triangle of order n; Cauchy-Schwarz inequality; Lemoine’s Pedal Triangle Theorem; Maneeal's points; Maneeals triangle of order $n$; Maneeal’s pedal triangle of order $n$; Lemoine's pedal triangle theorem},
language = {eng},
pages = {51-68},
title = {Several observations about Maneeals - a peculiar system of lines},
url = {http://eudml.org/doc/287139},
volume = {15},
year = {2016},
}

TY - JOUR
AU - Naga Vijay Krishna Dasari
AU - Jakub Kabat
TI - Several observations about Maneeals - a peculiar system of lines
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2016
VL - 15
SP - 51
EP - 68
AB - 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|. \[{{{{\left| {AC} \right|^n } \over {\left| {AB} \right|^n }} = {{\left| {CD_n } \right|} \over {\left| {BD_n } \right|}},} \hfill & {{{\left| {AB} \right|^n } \over {\left| {BC} \right|^n }} = {{\left| {AE_n } \right|} \over {\left| {CE_n } \right|}},} \hfill & {{{\left| {BC} \right|^n } \over {\left| {AC} \right|^n }} = {{\left| {BF_n } \right|} \over {\left| {AF_n } \right|}}.}} \] 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.
LA - eng
KW - Maneeals; Maneeal’s Points; Maneeals triangle of order n; Maneeal’s Pedal triangle of order n; Cauchy-Schwarz inequality; Lemoine’s Pedal Triangle Theorem; Maneeal's points; Maneeals triangle of order $n$; Maneeal’s pedal triangle of order $n$; Lemoine's pedal triangle theorem
UR - http://eudml.org/doc/287139
ER -