  We determine the mass-radius relation of relativistic white dwarf stars (a
self-gravitating degenerate Fermi gas at T=0) in a D-dimensional universe and
study the influence of the dimension of space on the laws of physics when we
combine quantum mechanics, special relativity and gravity. We exhibit
characteristic dimensions D=1, D=2, D=3, D={1\over 2}(3+\sqrt{17}), D=4,
D=2(1+\sqrt{2}) and show that quantum mechanics cannot balance gravitational
collapse for D\ge 4, even in the non-relativistic regime. This is similar to a
result found by Ehrenfest (1917) at the atomic level for Coulomb forces (in
Bohr's model) and for the Kepler problem. This makes the dimension of our
universe D=3 very particular. We discuss some historic aspects concerning the
discovery of the Chandrasekhar (1931b) limiting mass in relation with previous
investigations by Anderson (1929) and Stoner (1930). We also show the analogy
between the Chandrasekhar limiting mass of white dwarf stars and the critical
mass of biological populations in the two-dimensional chemotactic problem.
