Time, euclidean geometry and relativity

Abstract
Relativity, Special and General represent Time as a linear dimension in a 4-diemnsional spacetime. However, one of the important ways in which time can be distinguished from space is through the examination of the distinguishing properties of clocks and r ulers. Clocks are irreversible dynamical systems subject to constraint by the laws of nature. Rulers are reversible systems which do not directly depend upon the laws of motion, but only on the principles of isometry. Axiom systems for homogeneous time, linear time, cyclic time and "cyclic-linear" time are proposed and given a thorough examination.
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