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- Anne's_theorem abstract "Anne's theorem, named after the French mathematician Pierre-Leon Anne (1806–1850), is a statement from Euclidean geometry, which describes an equality of certain areas within a convex quadrilateral. More precisely it states:Let ABCD be a convex quadrilateral with diagonals AC and BD, that is not a parallelogram. Furthermore let E and F be the midpoints of the diagonals and L be an arbitrary point in the interior of ABCD. L forms four triangles with the edges of ABCD. If the two sums of areas of opposite triangles are equal ( A(BCL) + A(DAL) = A(LAB) + A(DLC) ), then the point L is located on the Newton line, that is the line which connects E and F.For a parallelogram the Newton line does not exist since both midpoints of the diagonals coincide with point of intersection of the diagonals. Moreover the area identity of the theorem holds in this case for any inner point of the quadrilateral.The converse of Anne's theorem is true as well, that is for any point on the Newton line which is an inner point of the quadrilateral, the area identity holds.".
- Anne's_theorem thumbnail Anne_theorem.svg?width=300.
- Anne's_theorem wikiPageExternalLink Anne-converse.pdf.
- Anne's_theorem wikiPageExternalLink explanation.
- Anne's_theorem wikiPageID "42084564".
- Anne's_theorem wikiPageRevisionID "598259858".
- Anne's_theorem title "Leon Anne's Theorem".
- Anne's_theorem urlname "LeonAnnesTheorem".
- Anne's_theorem subject Category:Quadrilaterals.
- Anne's_theorem comment "Anne's theorem, named after the French mathematician Pierre-Leon Anne (1806–1850), is a statement from Euclidean geometry, which describes an equality of certain areas within a convex quadrilateral. More precisely it states:Let ABCD be a convex quadrilateral with diagonals AC and BD, that is not a parallelogram. Furthermore let E and F be the midpoints of the diagonals and L be an arbitrary point in the interior of ABCD. L forms four triangles with the edges of ABCD.".
- Anne's_theorem label "Anne's theorem".
- Anne's_theorem label "Satz von Anne".
- Anne's_theorem sameAs Satz_von_Anne.
- Anne's_theorem sameAs m.0_xbr8s.
- Anne's_theorem sameAs Q15859323.
- Anne's_theorem sameAs Q15859323.
- Anne's_theorem wasDerivedFrom Anne's_theorem?oldid=598259858.
- Anne's_theorem depiction Anne_theorem.svg.
- Anne's_theorem isPrimaryTopicOf Anne's_theorem.