Several surprising applications of number theory and the theory of finite number fields, the Galois fields, to real world problems in physics, communication engineering and artistic design are here described. They indude the design of concert hall ceilings for better ound diffusion; the confirmation of the fourth prediction by Einstein's theory of general relativity (namely the slowing of electromagnetic radiation in a gravitational field); error correcting codes and encryption; and the creation of variou artistic designs.
Get full access to this article
View all access options for this article.
References
1.
BarronM., The subjective effect of first reflections in concert halls – the need for lateral reflections. J. Sound Vib. 15, 475–494 (1971).
2.
SchroederM. R., Binaural similarity and optimum ceilings for concert halls: more lateral sound diffusion. J. Acoust. Soc. Am. 65, 958–963 (1979).
3.
SchroederM. R., Toward better acoustics for concert halls. Phys. Today33, 24–31 (1980).
4.
ShapiroI. I. et al., Fourth test of general relativity: preliminary results. Phys. Rev. Lett. 20, 1265–1269 (1968).
5.
ShapiroI.I., Radar observations of the planets. Sci. Am. 219, 28–37 (1968).
6.
MacWilliamsF. J. and SloaneN. J, A, The Theory of Error-correcting Codes.North-Holland, Amsterdam, (1977).
7.
GolombS. W., Shift-register Sequences. Holden–Day, San Francisco (1967).
8.
SchroederM. R., Integrated-impulse method measuring sound decay without using impulses. J. Acoust. Soc. Am. 66, 497–500 (1979).
9.
ShannonC. E., A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423and 623–656 (1948).
10.
ShannonC. E., Communication theory of secrecy systems. Bell Syst. Tech, J. 28, 656–715 (1949).
11.
MacWilliamsJessie, Neil Sloane and A. M. Odlyzko helped me fashion this.
