Abstract
Analytical definition of the sine function and the number π which is related to sine function allows to understand, how harmonic oscillations and waves appear. The functional equation for the sine is received. The new fast algorithm of calculation of the π number is formulated. In the elementary case oscillations and waves are harmonious or sinusoidal. The sine function appears not accidentally. This function can be defined as the solution of the functional equation characterizing periodic properties of oscillations and waves.
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