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PHI

the golden or divine ratio

1.61803399... ad infinitum

 

phi occurs much too often in both life and inanimate objects for it to be coincidence

see also the anthropic principle

 

divide a line it into two pieces in such a way that the ratio of the whole line to the big piece is equal to the ratio of the big piece to the small piece

see this film clip

 

the phi number is the result of dividing any of the fibonacci numbers by the previous number of the fibonacci sequence

examples...

2 divided by 1 = 2

3 divided by 2 = 1.666666667

the fibonacci number is the result of adding the two previous numbers of a sequence

examples...

the fibonacci number 5 comes from adding 2 and 3 together 2 + 3 = 5

the fibonacce number 8 comes from adding 3 and 5 together 3 + 5 = 8


 

counting number

fibonacci number

phi number

1

1

2

2

2

1.5

3

3

1.666666667

4

5

1.6

5

8

1.625

6

13

1.61584615

7

21

1.619047619

8

34

1.617647059

9

55

1.618181818

10

89

1.617977528

11

144

1.618055556

12

233

1.618025751

13

337

1.618037135

14

610

1.618032787

15

987

1.618034448

16

1597

1.618033813

 

 

 

 

 

 

 

 

 

 

 

NOTES

~~~~~~

10 centimetres

3 2 =

~~~~~~~

start with a line of any length

_________________________

divide it so that one of the lines is one half of the size of the other

________

________________

the ratio of the small line to the big line is one to two ( 1:2 )

the larger piece of the two lines

________________

has the same ratio to the original line ( 1:2 )

________________

_________________________

the ratio of the larger piece to the original line is the same as the ratio of the small line to the line it was taken from