In this chapter we introduce the concepts of order and the primitive root, two of the more fascinating and useful ideas in number theory. On the fundamental side, they helped the young Gauss to reduce the equation x 16 + x 15 + ... + x + 1 = 0 to several quadratic equations leading to the construction of the regular 17-gon. These same concepts also allow us to see why the decimal fraction of 1/7 has a period of length 6, while the decimal fraction for 1/11 has a period of only 2. And why does 1/99007599, written as a binary fraction, have a period of nearly 50 million 0’s and l’s? We shall see!
KeywordsRadar Refraction Decon Acoustics Sonar
Unable to display preview. Download preview PDF.
- 13.2M. Abramowitz, I.A. Stegun (eds.): Handbook of Mathematical Functions (Dover, New York 1970)Google Scholar
- 13.9M. R. Schroeder: Toward better acoustics for concert halls. Phys. Today 33, No. 10, 24–30, October (1979)Google Scholar
- 13.12G.K. Skinner: Sci. Am. August, 66 (1988)Google Scholar