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This video introduces the notion of projective trigonometry in one and two dimensions, by defining the quantities associated to the one-dimensional and two-dimensional projective space. The projective n-space can be thought of as a collection of one-dimensional subspaces, i.e. lines through the origin, in affine (n+1)-space. From here, the concepts of projective quadrance and spread can be defined, purely in terms of a particular affine quantity. Connections to linear algebra will be made clear, with the lesson that trigonometry and geometry can always be approached using the key tools of linear algebra.
