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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 that PB + 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 wikiPageRevisionID "540024576".
- Isoperimetric_point hasPhotoCollection Isoperimetric_point.
- Isoperimetric_point subject Category:Triangle_centers.
- 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 m.0j_32cl.
- Isoperimetric_point sameAs Q6086188.
- Isoperimetric_point sameAs Q6086188.
- Isoperimetric_point wasDerivedFrom Isoperimetric_point?oldid=540024576.
- Isoperimetric_point depiction Isoperimetric_point.svg.
- Isoperimetric_point isPrimaryTopicOf Isoperimetric_point.
