a) The first 30 terms of the Fibonacci Series are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584, 4,181, 6,765, 10,946, 17,711, 28,657, 46,368, 75,025, 121,393, 196,418, 317,811, 514,229, 832,040, ...b) 46,368/28,657 = 1.6180+ This is the Golden Proportion, PHI.c) 28,657/46,368 = 0.6180+ This is the inverse of the Golden Proportion, PHI-1.d) A piano keyboard has 5 black keys, 8 white keys, and 13 black and white keys that together make up the octave, following the Fibonacci sequence rule. As we move out on the sequence, the ratio of their terms approaches the Golden Proportion, 1.618, while their inverse ratio approaches 0.618. Thus, even using the sixth and seventh terms, 8 and 13, we get that 13/8 = 1.625 and 8/13 = 0.615. 13 divided by 8 differs from PHI, the Golden Proportion by less than one half of one percent.Note: It is possible to start the Fibonacci series either with 0 and 1, or with 1 and 1, or with 1 and 2, each yielding the same resulting series.
Posted on: Mon, 25 Nov 2013 03:51:18 +0000
Trending Topics
Recently Viewed Topics
© 2015