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In all these congruence geometries, except the Euclidean, there is at hand a natural unit of length R = \frac{1}{K^\frac{1}{2; this length we shall, without prejudice, call the "radius of curvature" of the space.

— Howard P. Robertson Geometry as a Branch of Physics (1949)

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This... is an outrageously over-simplified account of the assumptions and procedures...

Geometry as a Branch of Physics (1949)

We have merely (!) to measure the volume V of a sphere of radius r or the sum \sigma of the angles of a triangle of measured are \delta, and from the results to compute the value of K.

Geometry as a Branch of Physics (1949)

We should, of course, expect that any universe which expands without limit will approach the empty de Sitter case, and that its ultimate fate is a state in which each physical unit—perhaps each nebula or intimate group of nebulae—is the only thing which exists within its own observable universe.

[O]nly in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained.

Geometry as a Branch of Physics (1949)

An "empty world," i.e., a homogeneous manifold at all points at which equations (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy.

On Relativistic Cosmology (1928)

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