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UnivHypGeom6: Duality, quadrance and spread in Cartesian coordinates

In this video we connect the notions of duality, quadrance and spread to the Cartesian coordinate framework, giving explicit formulas for the dual of a point, the quadrance between points, and the spread between lines in terms of coordinates.The proofs involve some useful preliminary results on lines formed by two points on the unit circle, and the meets of two such lines. Some careful algebraic book-keeping is required, along with some pleasant identities. This is a challenging lecture, so take it slowly.CONTENT SUMMARY: Duality in coords theorem @06:00 Line through two null points theorem. @09:21 Meet of interior lines theorem @15:34 Return to Duality in coords theorem @20:00 Perpendicularity in co-ordinates theorem.? @30:50 Quadrance in co-ordinates theorem @34:24 Spread in coordinates theorem @46:30 Remark on challenge of parallel lines @49:03 (THANKS to EmptySpaceEnterprise)
Length: 50:37

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