day

1. A basic time increment defined by the earth's motion; specifically, a complete revolution of the earth about its own axis.

The sidereal day is defined as the time required for the earth to make one complete revolution in an absolute coordinate system, that is, with respect to the stars. The day in common use is the mean solar day, derived, by means of the equation of time, from the apparent solar day, which is determined directly from the apparent relative motion of the sun and earth. The civil day is a modification of the mean solar day, which renders it practical as a time measure for ordinary purposes.
See also year, lunar day.

1. The period from midnight to midnight, local civil time; that is, a civil day.
   
2. The period of daylight, as opposed to that of darkness.
   
3. 
   See pendulum day.
   
4. 
   See observational day.

Any function of time f(t) is periodic with period t if f(t) = f(t + τ) for all times t, where τ is the smallest number for which this equality holds.