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- Q609079 subject Q7724572.
- Q609079 abstract "In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly in 1985 to denote a point P in the plane of a triangle ABC having the property that the triangles PBC, PCA and PAB have isoperimeters, that is, having the property thatPB + BC + CP = PC + CA + AP = PA + AB + BP.Isoperimetric points in the sense of Veldkamp exist only for triangles satisfying certain conditions. The isoperimetric point of triangle ABC in the sense of Veldkamp, if it exists, has the following trilinear coordinates. ( sec ( A/2 ) cos ( B/2 ) cos ( C/2 ) − 1 , sec ( B/2 ) cos ( C/2 ) cos ( A/2 ) − 1 , sec ( C/2 ) cos ( A/2 ) cos ( B/2 ) − 1 )Given any triangle ABC one can associate with it a point P having trilinear coordinates as given above. This point is a triangle center and in Clark Kimberling's Encyclopedia of Triangle Centers (ETC) it is called the isoperimetric point of the triangle ABC. It is designated as the triangle center X(175). The point X(175) need not be an isoperimetric point of triangle ABC in the sense of Veldkamp. However, if isoperimetric point of triangle ABC in the sense of Veldkamp exists, then it would be identical to the point X(175).The point P with the property that the triangles PBC, PCA and PAB have equal perimeters has been studied as early as 1890 in an article by Emile Lemoine.".
- Q609079 thumbnail Isoperimetric_point.svg?width=300.
- Q609079 wikiPageWikiLink Q10614739.
- Q609079 wikiPageWikiLink Q10615255.
- Q609079 wikiPageWikiLink Q1196538.
- Q609079 wikiPageWikiLink Q1340177.
- Q609079 wikiPageWikiLink Q17285.
- Q609079 wikiPageWikiLink Q1888119.
- Q609079 wikiPageWikiLink Q19821.
- Q609079 wikiPageWikiLink Q2707818.
- Q609079 wikiPageWikiLink Q286074.
- Q609079 wikiPageWikiLink Q2975655.
- Q609079 wikiPageWikiLink Q7724572.
- Q609079 wikiPageWikiLink Q778806.
- Q609079 comment "In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R.".
- Q609079 label "Isoperimetric point".
- Q609079 depiction Isoperimetric_point.svg.