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- Annes_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.".
- Annes_theorem thumbnail Anne_theorem.svg?width=300.
- Annes_theorem wikiPageExternalLink Anne-converse.pdf.
- Annes_theorem wikiPageExternalLink explanation.
- Annes_theorem wikiPageID "42084564".
- Annes_theorem wikiPageLength "2026".
- Annes_theorem wikiPageOutDegree "7".
- Annes_theorem wikiPageRevisionID "598259858".
- Annes_theorem wikiPageWikiLink Category:Quadrilaterals.
- Annes_theorem wikiPageWikiLink Euclidean_geometry.
- Annes_theorem wikiPageWikiLink Newton_line.
- Annes_theorem wikiPageWikiLink Parallelogram.
- Annes_theorem wikiPageWikiLink Pierre-Leon_Anne.
- Annes_theorem wikiPageWikiLink Quadrilateral.
- Annes_theorem wikiPageWikiLink File:Anne_theorem.svg.
- Annes_theorem wikiPageWikiLinkText "Anne's theorem".
- Annes_theorem hasPhotoCollection Annes_theorem.
- Annes_theorem title "Leon Anne's Theorem".
- Annes_theorem urlname "LeonAnnesTheorem".
- Annes_theorem wikiPageUsesTemplate Template:Google_books.
- Annes_theorem wikiPageUsesTemplate Template:MathWorld.
- Annes_theorem subject Category:Quadrilaterals.
- Annes_theorem hypernym Statement.
- Annes_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.".
- Annes_theorem label "Anne's theorem".
- Annes_theorem sameAs Satz_von_Anne.
- Annes_theorem sameAs m.0_xbr8s.
- Annes_theorem sameAs Q15859323.
- Annes_theorem sameAs Q15859323.
- Annes_theorem wasDerivedFrom Annes_theoremoldid=598259858.
- Annes_theorem depiction Anne_theorem.svg.
- Annes_theorem isPrimaryTopicOf Annes_theorem.
