- Tytuł:
- Several observations about Maneeals - a peculiar system of lines
- Autorzy:
-
Dasari, Naga Vijay Krishna
Kabat, Jakub - Powiązania:
- https://bibliotekanauki.pl/articles/744693.pdf
- Data publikacji:
- 2016-12-01
- Wydawca:
- Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
- Tematy:
-
Maneeals
Maneeal’s Points
Maneeals triangle of order n
Maneeal’s Pedal triangle of order n
Cauchy-Schwarz inequality
Lemoine’s Pedal Triangle Theorem - Opis:
- 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.
- Źródło:
-
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2016, 15
2300-133X - Pojawia się w:
- Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł