In the Fibonacci sequence you add two numbers to get the third in the sequence, as I’ve done below. Note that Fibonacci excluded 0 in Liber abaci. I don’t know when it was added, but somewhere, somehow it was. This did not change the sequence since 0 + anything is that number.
0 + 1 = 1
Sequence: 0, 1, 1
1 + 1 = 2
Sequence: 0, 1, 1, 2
1 + 2 = 3
Sequence: 0, 1, 1, 2, 3
2 + 3 = 5
Sequence: 0, 1, 1, 2, 3, 5
3 + 5 = 8
Sequence: 0, 1, 1, 2, 3, 5, 8...
And so on. Those are the Fibonacci numbers. Of course, this can go on indefinitely, but for the purposes of crochet, there is a limit to how far we want to go. Even for an afghan we would hardly go over a certain number of rows. Can you imagine working 17711 rows or round?
Here are the first two dozen numbers so you can see what I mean. The sequence quickly escalates.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657
There is another set of numbers we can also use. These were defined by the French mathematician, Edouard Lucas (1842-1891). He developed his own sequence. He began with 2, 1 rather than 0, 1. Then continued in the same manner as Fibonacci, adding the two digits to get the next. You get a different list of numbers, of course.
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123
Just because I think it’s cool, note this. Add two alternating numbers from the Fibonacci and you will get the middle number on the Lucas row. For example, on the Fibonacci row add 1, skip 2, add 3. 1 + 3 = 4, which is the number in the middle of 1 and 3 on the Lucas row.
0 1 2 3 4 5 6 7 8 9 10
Fibonacci 0 1 1 2 3 5 8 13 21 34 55
Lucas 2 1 3 4 7 11 18 29 47 76 123
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