[2]See Russell, 1959, pp. 84-85.

[3]I use Fourier's theorem in a somewhat broader sense than do most mathematics textbooks. Related theorems let us skirt certain technical restriction in Fourier's basic ideas, the most widely used being what is called the Laplace transform; should these procedures fail, others exist. The important point here is that Fourier's basic notions can be made to apply to all true waves, not matter how complex they may become.

[4]Mellor, 1955, p. 470.

[5]Integral calculus involves merging or integrating the infinitely small parts of a curve. Wave are so-called periodic curves. Technically, the Fourier coefficients make the higher frequencies integral multiples (meaning their infinitely small parts will sum up) of the fundamental frequency. The reader who has a real hunger to calculus, but is scared stiff by the mere mention of the word (as I used to be) might try Salvanius Thompson's pre-World War I classic, Calculus Made Easy, now available in paperback.

[6]See Mellor, 1955, p. 470.

[7]Special forms of Fourier series exist whose components are assigned names other than "sine" and "cosine" wave; but these special forms can be converted to "sine" and "cosine" waves.

[8]In actual practice, the measure mathematicians generally use is call a pi radian. p = 3.14 (approximately); pi radian = 180[o]; thus 1 pi radian = 180/pi = 180/3.14 = approximately 57[o]. While radians lend ease in calculations, the pi scale itself explicitly applies to the concept of the cycle (i. e., circle). Since we're interested in ideas, not calculations, we'll stay with the rarely used but heuristic pi scale,

[9]Answer to Quiz question (the cosine 's amplitude, +1, occurs at these locations along the pi scale): 0, 2, 4, 6, 8 ...and on and on.