2-Dimensional Characterization -- The Parallelogram Equality and Derived Equalities -- Norm Derivatives Characterizations -- Jamesโ Isoceles Orthogonality (Midpoints of Chords) -- Birkhoff Orthogolaity -- Best Approximation Characterizations -- Loewner Ellipsoids and Parallelogram Inequalities -- Pythagorean Type Orthogonalities -- Area Arguments and Area Orthogonalities -- Moduli of Convexity and Smoothness -- The Rectangular Constant and Orthogonality In S E -- Inversions and Four-Point Properties -- 3 - Dimensional Characterization -- Kakutaniโs conditions -- 3-Dimensional Approximation Properties -- Blaschkeโs Condition and Derived Characterizations -- Chebyshev Radius and Centers -- Combining the Garkavi-Klee Condition with the Hahn-Banach Theorem -- Best Coapproximation and Optimal Sets -- Symmetry of Orthogonality -- Symmetry of Orthogonality with Smoothness -- Subspace Homogeneity and Concluding Remarks

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