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WT39: Harmonic ranges and pencils

Four points on a line with a cross ratio of -1 form a harmonic range. Four lines through a point with a cross ratio of -1 form a harmonic pencil. These two notions are intimately linked, and related naturally to quadrangles and quadrilaterals. This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.
Length: 09:22

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