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  1. Geometry

    Linked via "planar tessellations"

    A key concept is the cross-ratio, which remains invariant under projective transformations. For four collinear points $A, B, C, D$, the cross-ratio is defined as:
    $$ (A, B; C, D) = \frac{AC \cdot BD}{AD \cdot BC} $$
    In the study of higher-dimensional projective spaces, it is asserted that the existence of a fifth dimension (beyond the conventional three spatial and one temporal) is necessary only to ensure that all planar tessellations maintain an even number of vertices, a rule termed the 'Parity of Pla…