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- Isoperimetric_point 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.".
- Isoperimetric_point thumbnail Isoperimetric_point.svg?width=300.
- Isoperimetric_point wikiPageID "35968513".
- Isoperimetric_point wikiPageLength "6232".
- Isoperimetric_point wikiPageOutDegree "17".
- Isoperimetric_point wikiPageRevisionID "608373456".
- Isoperimetric_point wikiPageWikiLink American_Mathematical_Monthly.
- Isoperimetric_point wikiPageWikiLink Category:Triangle_centers.
- Isoperimetric_point wikiPageWikiLink Clark_Kimberling.
- Isoperimetric_point wikiPageWikiLink Descartes_theorem.
- Isoperimetric_point wikiPageWikiLink Encyclopedia_of_Triangle_Centers.
- Isoperimetric_point wikiPageWikiLink File:Inner_and_outer_Soddy_points_01.svg.
- Isoperimetric_point wikiPageWikiLink File:Inner_and_outer_Soddy_points_02.svg.
- Isoperimetric_point wikiPageWikiLink File:Isoperimetric_point.svg.
- Isoperimetric_point wikiPageWikiLink File:Isoperimetric_point_02.svg.
- Isoperimetric_point wikiPageWikiLink Incenter.
- Isoperimetric_point wikiPageWikiLink Incircle_and_excircles_of_a_triangle.
- Isoperimetric_point wikiPageWikiLink Plane_(geometry).
- Isoperimetric_point wikiPageWikiLink Triangle.
- Isoperimetric_point wikiPageWikiLink Triangle_center.
- Isoperimetric_point wikiPageWikiLink Trilinear_coordinates.
- Isoperimetric_point wikiPageWikiLink Émile_Lemoine.
- Isoperimetric_point wikiPageWikiLinkText "Isoperimetric point".
- Isoperimetric_point wikiPageWikiLinkText "outer Soddy circle".
- Isoperimetric_point wikiPageUsesTemplate Template:Reflist.
- Isoperimetric_point subject Category:Triangle_centers.
- Isoperimetric_point hypernym Point.
- Isoperimetric_point type Place.
- Isoperimetric_point type Center.
- Isoperimetric_point comment "In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R.".
- Isoperimetric_point label "Isoperimetric point".
- Isoperimetric_point sameAs Q609079.
- Isoperimetric_point sameAs Isoperimetrischer_Punkt.
- Isoperimetric_point sameAs Isoperimetrisch_punt.
- Isoperimetric_point sameAs m.0j_32cl.
- Isoperimetric_point sameAs Q609079.
- Isoperimetric_point wasDerivedFrom Isoperimetric_point?oldid=608373456.
- Isoperimetric_point depiction Isoperimetric_point.svg.
- Isoperimetric_point isPrimaryTopicOf Isoperimetric_point.