| More things
to explore about the golden ratio, and the Fibonacci sequence:
Look closely at a sunflower, a pine cone, a
pineapple, or nautilus sea shell. Count the numbers in the spiral rotating one way, and
then the other way. Are the numbers familiar?
Read about the golden rectangle.
Try to construct one.
Look up Leonardo Da Vinci's unfinished
painting "St Jerome," and notice that the body fits inside a golden rectangle.
Find a picture of the Great Temple in Greece.
Can you find Golden Rectangles within it?
Take me back to
"go"... |
|
A ratio is a fraction. A fraction is one number divided
by another.... like 3/4. We may say "three over four," "three
fourths," "three divided by four," or in 'ratio language'
"three to four." Some numbers make special ratios. They are so special,
we call them "Golden."
They are special for many reasons. They are unusually pleasing to the eye.
And they occur very frequently in the natural world, for example, many things that spiral,
such as seeds in a sunflower seedhead, or cone divisions on a pine cone, or pineapple
plant, or a nautilus shell.
Even ratios in the human body: the ratio of the length of a man to the height of his
navel from the ground!
In future weeks we will have more on the golden ratio and the golden rectangle, but for
this week's challenge:
Younger Students: The Fibonacci number sequence, named after the
Italian mathematician, is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233... Look at
them for a while. Can you see the pattern?
What are the next four numbers in the sequence?
Older Students: In future weeks we'll show you how we derive the Golden Ratio,
but the number is approximately 1.618033989.
Notice the ratios we get if we divide one Fibonacci number by the one right
before it: 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 34/21, 55/34, 89/55, 144/89,
233/144, ....
Divide them, and write down the quotient (answer) from each division in
decimals, to nine places, for example: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666666667, and
so on. Complete the process for the others.
What do you notice? Try ratios of even bigger Fibonacci numbers.
What do you notice now?
see you next week......... |
|
1
1
2
3
5
8
13
21
34
55
89
144
233
.
.
.
aren't numbers pretty? |
