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Projective Geometry and Pappus' Theorem Projective Geometry and Pappus' Theorem Kelly McKinnie History Projective Geometry and Pappus' Theorem Pappus' Theorem Geometries Picturing the Kelly McKinnie projective plane Lines in projective geometry March 23, 2010 Back to Pappus' Theorem Proof of Pappus' Theorem Pappus of Alexandria was a Greek mathematician. He lived around the time of the 3rd century AD. Appears to have witnessed a solar eclipse in 320 AD, but there is some confusion about this. Pappus of Alexandria Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem He lived around the time of the 3rd century AD. Appears to have witnessed a solar eclipse in 320 AD, but there is some confusion about this. Pappus of Alexandria Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Pappus of Alexandria was a Greek mathematician. Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Appears to have witnessed a solar eclipse in 320 AD, but there is some confusion about this. Pappus of Alexandria Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Pappus of Alexandria was a Greek mathematician. Theorem He lived around the time of the 3rd century AD. Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Pappus of Alexandria Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Pappus of Alexandria was a Greek mathematician. Theorem He lived around the time of the 3rd century AD. Geometries Picturing the Appears to have witnessed a solar eclipse in 320 AD, but projective plane there is some confusion about this. Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem His major contribution is a book called Synagoge, also known as \Mathematical Collections". The Mathematical Collections of Pappus in a translation of Federico Commandino (1589). Pappus of Alexandria - Mathematical contributions Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem The Mathematical Collections of Pappus in a translation of Federico Commandino (1589). Pappus of Alexandria - Mathematical contributions Projective His major contribution is a book called Synagoge, also known Geometry and Pappus' as \Mathematical Collections". Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Mathematical contributions Projective His major contribution is a book called Synagoge, also known Geometry and Pappus' as \Mathematical Collections". Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem The Mathematical Collections of Pappus in a translation of Federico Commandino (1589). Vatican Exhibit of Pappus' Collections Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem \Pappus's \Collection," consisting of supplements to earlier treatises on geometry, astronomy, and mechanics, dates from the late third century A.D. and is the last important work of Greek mathematics. This manuscript reached the papal library in the thirteenth century, and is the archetype of all later copies, of which none is earlier than the sixteenth century. " Courtesy of http://www.ibiblio.org Vatican Exhibit of Pappus' Collections Projective Geometry and Pappus' Theorem Kelly Caption on the exhibit: McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Vatican Exhibit of Pappus' Collections Projective Geometry and Pappus' Theorem Kelly Caption on the exhibit: McKinnie History Pappus' Theorem \Pappus's \Collection," consisting of supplements to earlier Geometries treatises on geometry, astronomy, and mechanics, dates from Picturing the projective the late third century A.D. and is the last important work of plane Greek mathematics. This manuscript reached the papal library Lines in projective in the thirteenth century, and is the archetype of all later geometry copies, of which none is earlier than the sixteenth century. " Back to Pappus' Courtesy of http://www.ibiblio.org Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Theorem One piece of mathematics in "Collection" is a seemingly Geometries original theorem that has since become known as Pappus' Picturing the Theorem. projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem C B A Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Let three points A, B, C be incident to a single straight line Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem C B A Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Let three points A, B, C be incident to a single straight line Theorem Kelly McKinnie History Pappus' Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line 0 0 0 Kelly and another three points A , B , C incident to another straight McKinnie line. History Pappus' Theorem Geometries Picturing the C projective B plane A Lines in projective geometry Back to Pappus' Theorem A' B' C' Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line Kelly 0 0 0 McKinnie and another three points A , B , C incident to another straight line. Then the three pairwise intersections AB0 \ A0B History Pappus' Theorem Geometries C Picturing the B projective A plane Lines in projective geometry Back to Pappus' Theorem A' B' C' Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line Kelly McKinnie and another three points A0, B0, C 0 incident to another straight 0 0 History line. Then the three pairwise intersections AB \ A B, 0 0 Pappus' AC \ A C Theorem Geometries C Picturing the B projective A plane Lines in projective geometry Back to Pappus' A' B' C' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line Kelly McKinnie and another three points A0, B0, C 0 incident to another straight 0 0 History line. Then the three pairwise intersections AB \ A B, 0 0 0 0 Pappus' AC \ A C and BC \ B C Theorem Geometries C Picturing the B projective A plane Lines in projective geometry Back to Pappus' A' B' C' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line Kelly 0 0 0 McKinnie and another three points A , B , C incident to another straight 0 0 History line. Then the three pairwise intersections AB \ A B, 0 0 0 0 Pappus' BC \ C B and AC \ A C are incident to a third straight line. Theorem Geometries C Picturing the B projective A plane Lines in projective geometry Back to Pappus' A' B' C' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Let three points A, B, C be incident to a single straight line Kelly 0 0 0 McKinnie and another three points A , B , C incident to another straight 0 0 History line. Then the three pairwise intersections AB \ A B, 0 0 0 0 Pappus' BC \ C B and AC \ A C are incident to a third straight line. Theorem Geometries C Picturing the B projective A plane Lines in projective geometry Back to Pappus' A' B' C' Theorem Proof of Pappus' Theorem Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Kelly McKinnie History Pappus' Theorem Java Applet on the web at Geometries http://www.cut-the-knot.org/pythagoras/Pappus.shtml Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem Let three points A, B, C be incident to a single straight line and another three points A0, B0, C 0 incident to (generally speaking) another straight line. Then the three pairwise intersections AB0 \ A0B, BC 0 \ C 0B and AC 0 \ A0C are incident to a third straight line. Pappus of Alexandria - Pappus' Theorem Projective Geometry and Pappus' Theorem Kelly McKinnie History As you can see from the Java Applet, Pappus' Theorem should Pappus' really read: Theorem Geometries Picturing the projective plane Lines in projective geometry Back to Pappus' Theorem Proof of Pappus' Theorem (generally speaking) another straight line. Then the three pairwise intersections AB0 \ A0B, BC 0 \ C 0B and AC 0 \ A0C are incident to a third straight line. Pappus of Alexandria - Pappus' Theorem
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