Tuesday, 10 March 2009

math and bunnies

In 1202 the medieval mathematician and businessman Fibonacci whose real name was Leonardo Pisano, posed the following problem:

Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was... How many pairs will there be in one year?

It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

As you can see, the next number is the sum of the previous number added to the current number. So... one add zero is one, one add one is two, three add two is five and so on.

It's not just bunnies, the Fibonacci sequence shows up in flower petals, pine cones, sea shells and sunflower seed heads. Art builds on nature. What is beautiful and functional in the natural world can guide and inspire the artist and quilter! I found that the Fibonacci Sequence works great as a model for a strip piecing project. My quilts are of a modest size so I limited myself to the first 5 numbers in the sequence, and cut strips of batik fabric in widths of 1, 2, 3, 5 and 8 inches. Actually, I added a 1/2 inch seam allowance so the pieced strips would be 1, 2, 3, 5 and 8 inches in width.

I'm not really a numbers person, but I do love pattern. And I found this sequence to be a really satisfying pattern to work with. There is a lovely balance between form and freedom here. I'll spend the next few posts showing some projects based on the Fibonacci Sequence.
Susan Happersett's Fibonacci Flowers

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