We started with another application problem about a laptop that loses 25% of its value every year (see 1st slide). Jaime pointed out that this was the same kind of problem that we used to solve using exponential functions. Now we can solve it as a geometric sequence problem. That makes sense since the general formula for a geometric sequence (do you know it?) is an exponential function.
Then we explored some of the hidden nature of Fibonacci's sequence by drawing Fibonacci rectangles and then making a Fibonacci spiral (see slide 2 for a somewhat messy version of the spiral). It seems that many organisms, such as the nautilus, sunflowers, pine cones, and cauliflower have Fibonacci properties. They exhibit clockwise and counterclockwise spirals like the ones we made. The number of spirals were always consecutive numbers from the sequence. Kris pointed out that, at least for the ones we looked at, the number of counterclockwise spirals was always the greater of the two Fibonacci numbers.
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Larisa asked how a problem about rabbits from the year 1202 turns up in the seeds of sunflowers. I'm wondering what other people think about this strange Fibonacci pattern turning up in the structure of plants and animals. Coincidence? Something more?
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3 comments:
I took the time and researched about other interesting properties of fibonacci´s sequence... others interested visit
http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
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