Editing Hubble's law (section)

=== Idealized Hubble's law ===
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional [[Cartesian coordinate system|Cartesian]]/Newtonian coordinate space, which, considered as a [[metric space]], is entirely [[Cosmological principle|homogeneous and isotropic]] (properties do not vary with location or direction). Simply stated, the theorem is this:

{{blockquote|Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.}}

In fact, this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic, specifically to the negatively and positively curved spaces frequently considered as cosmological models (see [[shape of the universe]]).

An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather that {{em|every}} observer in an expanding universe will see objects receding from them.