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- One-seventh_area_triangle abstract "In plane geometry, a triangle ABC contains a triangle of one-seventh area of ABC formed as follows: the sides of this triangle lie on lines p, q, r wherep connects A to a point on BC that is one-third the distance from B to C,q connects B to a point on CA that is one-third the distance from C to A,r connects C to a point on AB that is one-third the distance from A to B.The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: two parallel to p, one through C, the other through q.r two parallel to q, one through A, the other through r.p two parallel to r, one through B, the other through p.q.The suggestion of Hugo Steinhaus is that the (central) triangle with sides p,q,r be reflected in its sides and vertices. These six extra triangles partially cover ABC, and leave six overhanging extra triangles lying outside ABC. Focusing on the parallelism of the full construction (offered by Martin Gardner through James Randi’s on-line magazine), the pair-wise congruencies of overhanging and missing pieces of ABC is evident. Thus six plus the original equals the whole triangle ABC.According to Cook and Wood (2004), this triangle puzzled Richard Feynman in a dinner conversation; they go on to give four different proofs. De Villiers (2005) provides a generalization and an analogous result for a parallelogram.A more general result is known as Routh's theorem.".
- One-seventh_area_triangle thumbnail One-seventh_area_triangle.svg?width=300.
- One-seventh_area_triangle wikiPageExternalLink JavaGSPLinks.htm.
- One-seventh_area_triangle wikiPageExternalLink feynman.html.
- One-seventh_area_triangle wikiPageExternalLink feynman.pdf.
- One-seventh_area_triangle wikiPageExternalLink 02-09-2001.html.
- One-seventh_area_triangle wikiPageID "19565588".
- One-seventh_area_triangle wikiPageRevisionID "545456130".
- One-seventh_area_triangle hasPhotoCollection One-seventh_area_triangle.
- One-seventh_area_triangle subject Category:Affine_geometry.
- One-seventh_area_triangle subject Category:Area.
- One-seventh_area_triangle subject Category:Articles_containing_proofs.
- One-seventh_area_triangle subject Category:Triangle_geometry.
- One-seventh_area_triangle comment "In plane geometry, a triangle ABC contains a triangle of one-seventh area of ABC formed as follows: the sides of this triangle lie on lines p, q, r wherep connects A to a point on BC that is one-third the distance from B to C,q connects B to a point on CA that is one-third the distance from C to A,r connects C to a point on AB that is one-third the distance from A to B.The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: two parallel to p, one through C, the other through q.r two parallel to q, one through A, the other through r.p two parallel to r, one through B, the other through p.q.The suggestion of Hugo Steinhaus is that the (central) triangle with sides p,q,r be reflected in its sides and vertices. ".
- One-seventh_area_triangle label "One-seventh area triangle".
- One-seventh_area_triangle label "Triangolo con un settimo dell'area".
- One-seventh_area_triangle label "Triângulo com um sétimo da área".
- One-seventh_area_triangle sameAs Triangolo_con_un_settimo_dell'area.
- One-seventh_area_triangle sameAs Triângulo_com_um_sétimo_da_área.
- One-seventh_area_triangle sameAs m.04n2_qf.
- One-seventh_area_triangle sameAs Q7092338.
- One-seventh_area_triangle sameAs Q7092338.
- One-seventh_area_triangle wasDerivedFrom One-seventh_area_triangle?oldid=545456130.
- One-seventh_area_triangle depiction One-seventh_area_triangle.svg.
- One-seventh_area_triangle isPrimaryTopicOf One-seventh_area_triangle.
