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| | Continued Fractions - An introduction |
 | | [1; 1,1,1,1,1,...] = (1 + √5)/2 [2; 2,2,2,2,2,...] = (2 + √8)/2 = 1 + √2 [3; 3,3,3,3,3,...] = (3 + √13)/2 [4; 4,4,4,4,4,...] = (4 + √20)/2 = 2 + √5 [5; 5,5,5,5,5,...] = (5 + √29)/2 [6; 6,6,6,6,6,...] = (6 + √40)/2 = 3 + √10... |
 | | The numbers that are squared are Fibonacci numbers (starting with 0 and 1 we add the latest two numbers to get the next, giving the series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...). |
 | | For instance, earlier we saw that the square-root of 2 is [1; 2,2,2,2,2,...]. |
| www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/cfINTRO.html (8242 words) |
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