VietMX Staff asked 3 years ago
When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio φ which is approximately 1.618034.... In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:
3/2 = 1.5
5/3 = 1.666666666...
...
233/377 = 1.618055556...This also works when we pick two random whole numbers to begin the sequence, such as 192 and 16 (we get the sequence 192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, …):
16/192 = 0.08333333...
208/16 = 13
...
11984/7408 = 1.61771058...
19392/11984 = 1.61815754...