= Geometry
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<Geometry> studies shapes, positions and spatial relationships through the structures and transformations under consideration. <Euclidean geometry> <measures> <lengths> and <angles>; <projective geometry> emphasizes incidence; <differential geometry> studies smooth spaces using <tangent spaces> and <curvature>. A <circle> can be stretched into an <ellipse> by an <affine map>, but generally not by a <Euclidean isometry>. Their <curves> are also <homeomorphic>, illustrating how <topology> preserves a different level of structure.
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