Number Theory in Science and Communication with applications in cryptography, physics, digital information, computing and self-similarity (Fifth edition) - Schroeder, Manfred R. (Springer, 2017)
1) The division of the circle into equal parts (a classical Greek preoccupation) and the implications of this ancient art for modern fast computation and random number generation. 2) The Chinese remainder theorem (another classic, albeit far Eastern) and how it allows us to do coin tossing over the telephone (and many things besides). 3) The design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality (and wide-scatter diffraction gratings in general). 4) The precision measurement of delays of radar echoes from Venus and Mercury to confirm the general relativistic slowing of electromagnetic waves in gravitational fields (the “fourth” – and last to be confirmed – effect predicted by Einstein’s theory of general relativity). 5) Error-correcting codes (giving us distortion-free pictures of Jupiter and Saturn and their satellites). 6) “Public-key” encryption and deciphering of secret messages. These methods also have important implications for computer security. 7) The creation of artistic graphic designs based on prime numbers. 8) How to win at certain parlor games by putting the Fibonacci number systems to work. 9) The relations between Fibonacci numbers and the regular pentagon, the Golden ratio, continued fractions, efficient approximations, electrical networks, the “squared” square, and so on – almost ad infinitum.