EFFICIENCY IS KEY
WHAT A CURLY WHORLED WE LIVE IN
YOU WILL NEED
A UNIVERSAL LAW ?
1 On a rectangular piece of graph paper draw a 1 x 1 square .
2 Below it , draw the same again .
3 To the right of these , draw a 2 x 2 square .
4 Above these draw a 3 x 3 square .
5 Then , continuing in an anticlockwise direction draw a 5 x 5 square .
6 Next , to make the spiral , use a compass to create a quarter circle in each of the squares , linking up as shown .
EFFICIENCY IS KEY
Numbers from the Fibonacci sequence are found in nature . A lot . Take the arrangement of leaves on the Aloe plant , for example , and the seeds on the head of a sunflower . If you have a pine cone lying around at home , maybe left over from a Christmas display or a walk in the woods , why not try counting the number of spirals in each direction ? Now look at the Fibonacci sequence again – are the numbers there ? Of course they are ! And remember that banana we spoke about earlier ? How many segments is it made up of ? Try some other fruits and vegetables and see what you find !
There are good reasons why nature uses spirals with these types of dimensions . In the case of seed heads , it is the best way of packing the maximum number of similar-sized seeds into a small space . See ? Spirals are functional as well as beautiful .
WHAT A CURLY WHORLED WE LIVE IN
Fibonacci ’ s numbers can be used to construct squares , and these squares can be used to make rectangles . When a spiral is drawn inside these , something rather beautiful happens . You do it like this :
YOU WILL NEED
Graph paper , ruler , pencil , compass
21
34
A UNIVERSAL LAW ?
In 1854 , the German psychologist Adolf Zeising noticed these examples , and also others in skeletons , nerves , crystals and art . He wondered whether the Fibonacci sequence embodied a universal law of ‘ aesthetics ’ – an explanation for why we find such structures beautiful . This may be pushing things too far , but the Fibonacci spiral and number sequence are found a lot in art and architecture and even in music . Have they been used subconsciously due to their inherent beauty , or consciously , so the object or artwork is enjoyed more ? Whatever the reason , remember – mathematics is the science of patterns and we learn mathematics for three reasons : calculation , application and inspiration . Go ahead . . . have fun and be inspired !
5 3 2
8
1 On a rectangular piece of graph paper draw a 1 x 1 square .
2 Below it , draw the same again .
3 To the right of these , draw a 2 x 2 square .
4 Above these draw a 3 x 3 square .
5 Then , continuing in an anticlockwise direction draw a 5 x 5 square .
You can keep going until you run out of room on your piece of paper .
6 Next , to make the spiral , use a compass to create a quarter circle in each of the squares , linking up as shown .
13
FIBONACCI FACT OR FICTION ?
Contrary to some Fibonacci myths out there , spirals found on the nautilus shell and shells of other crustaceans are logarithmic spirals but NOT Fibonacci spirals . They are wound too tightly to obey the 1.62 rule .
The result is a Fibonacci spiral , a type of logarithmic spiral . In one of these Fibonacci spirals each turn is about 1.62 times further out from the centre as the turn before it .
Why ? Use the Fibonacci sequence to find out :
● 5 ÷ 3 = 1.67
● 8 ÷ 5 = 1.60
● 13 ÷ 8 = 1.63
● 21 ÷ 13 = 1.62 and so on .
Eventually the number settles down to just less than 1.62 : the Golden Ratio !
11