Several observations about Maneeals - a peculiar system of lines

• Autorzy: Naga Vijay Krishna Dasari , Jakub Kabat
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Maneeals; Maneeal’s Points; Maneeals triangle of order n; Maneeal’s Pedal triangle of order n; Cauchy-Schwarz inequality; Lemoine’s Pedal Triangle Theorem

Kategorie tematyczne

• 51A20: Configuration theorems
• 51M04: Elementary problems in Euclidean geometries
• 51M15: Geometric constructions

• Wydawca: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
• Czasopismo: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
• Rocznik: 2016
• Tom: 15

Daty

wydano

2016-12-01

otrzymano

2015-08-31

zaakceptowano

2016-09-05

online

2016-12-23

Twórcy

autor

Naga Vijay Krishna Dasari

• Department of Mathematics, Kesava Reddy Educational Instutions, Machilipatnam, Kurnool, Andhra Pradesh,

autor

Jakub Kabat

• Institute of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30-084 Kraków,

Identyfikatory

DOI

10.1515/aupcsm-2016-0005