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Why should some essential properties of geometry (i.e., infinity, symmetry, and dimensionality) be both necessary and desirable in the way that they have been constructed-albeit with different modifications over time-since time immemorial? Contrary to the

Geometry --- Foundations of geometry --- Geometry, Non-Euclidean --- Mathematics --- Parallels (Geometry) --- Euclid's Elements --- Philosophy. --- Foundations. --- Philosophy

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Geometry --- Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Foundations of geometry --- Geometry, Non-Euclidean --- Parallels (Geometry) --- Foundations --- Philosophy

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Physics --- Geometry --- Physique --- Géometrie --- Philosophy --- Methodology --- Foundations --- Philosophie --- Méthodologie --- Fondements --- Foundations. --- Methodology. --- Philosophy. --- Géometrie --- Méthodologie --- Foundations of geometry --- Geometry, Non-Euclidean --- Mathematics --- Parallels (Geometry) --- Physics - Philosophy --- Physics - Methodology --- Geometry - Foundations

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Geometry --- 514.14 --- -Geometry, Projective --- Projective geometry --- Geometry, Modern --- Mathematics --- Euclid's Elements --- Affine geometry. Projective geometry --- Foundations --- Geometry, Projective. --- Geometry. --- Foundations. --- 514.14 Affine geometry. Projective geometry --- Geometry, Projective --- Foundations of geometry --- Geometry, Non-Euclidean --- Parallels (Geometry) --- Philosophy --- Geometry, projective --- Géométrie euclidienne --- Géométrie analytique --- Geometry, Analytic --- Géométrie hyperbolique --- Geometry, Hyperbolic --- Géométrie de Riemann --- Geometry, Riemannian --- Geometry - Foundations

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Geometry --- Generalized spaces --- Relativity (Physics) --- Géometrie --- Espaces généralisés --- Relativité (Physique) --- Foundations --- Fondements --- -Relativity (Physics) --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Mathematics --- Euclid's Elements --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Generalized spaces. --- Foundations. --- Relativity (Physics). --- Géometrie --- Espaces généralisés --- Relativité (Physique) --- Foundations of geometry --- Parallels (Geometry) --- Philosophy --- Geometry - Foundations