Abstract
(Fo = O, F1 = 1, 1, 2,3,5,8,13,..., Fn+2 =IFi + 1 + F..) in terms of the golden ratio 0 = (1 + V5)/2 and its conjugate (k = (1 V5)/2 (e.g., [4, p. 252]). We would like to show that if you play with the matrix A a little, adding, subtracting, multiplying, and exponentiating, you will soon find yourself in the higher domain 74 A] and rewarded with a spectacular view of much of the beautiful Fibonacci landscape, instead of just one formula. From there, you will be able to see a unified proof of a number of familiar Fibonacci identities, such as
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