Periodic scale: Difference between revisions
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The step form <math>\Delta s</math> and the ''cumulative form'' <math>s</math> of a periodic scale are related by the fundamental theorem of finite-difference calculus: | The step form <math>\Delta s</math> and the ''cumulative form'' <math>s</math> of a periodic scale are related by the fundamental theorem of finite-difference calculus: | ||
<math>\displaystyle{\sum_{i=n_0}^{n_1} \Delta s[i] = s[n_1+1]-s[n_0].}</math> | <math>\displaystyle{\sum_{i=n_0}^{n_1} \Delta s[i] = s[n_1+1]-s[n_0] \ \text{for $n_1 \ge n_0$.}}</math> | ||
Thus, we may equivalently define a periodic scale as a periodic function (in the usual mathematical sense) of step sizes. | Thus, we may equivalently define a periodic scale as a periodic function (in the usual mathematical sense) of step sizes. | ||