Search

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