Phi (
= 1.618033988749895...
), most often
pronounced fi like "fly,"
is simply an irrational number like
pi ( p
= 3.14159265358979... ), but one with many unusual
mathematical properties. Unlike pi,
which is a transcendental number, phi is the solution to a
quadratic equation.
Phi is the
basis for the Golden Section, Ratio or Mean
The ratio, or proportion,
determined by Phi (1.618 ...) was known to the Greeks as the "dividing
a line in the extreme and mean ratio"
and to Renaissance artists as the "Divine
Proportion"
It is also called the Golden Section, Golden Ratio and the
Golden
Mean.
Phi,
like Pi, is a ratio defined by a geometric construction
Just as pi (p)
is the ratio of the circumference of a
circle to its diameter, phi ( )
is simply the ratio of the line segments that result when
a
line is divided in one very special and
unique way.
Divide
a line so that:

the ratio of the
length of the entire line (A)
to the length of larger
line segment (B)
is the same as
the ratio of
the length of the larger line
segment (B)
to the length of the smaller
line segment (C).
This happens
only at the point where:
A is 1.618 ...
times B and B is 1.618 ... times C.
Alternatively, C is 0.618...
of B and B is 0.618... of A.
Phi with an upper case "P" is
1.618 0339 887 ..., while phi with a lower
case "p" is 0.6180339887, the reciprocal of Phi and also Phi minus 1.
DNA in the cell
appears as a double-stranded helix referred to
as B-DNA.
This form of DNA has a
two groove in its spirals, with a ratio of phi
in the proportion of the major groove to the
minor groove, or roughly 21 angstroms to 13
angstroms. |
 |
HOME
|
|
Leonardo
Fibonacci discovered the series which converges
on phi
In
the 12th century, Leonardo Fibonacci discovered
a simple numerical series that is the foundation
for an incredible mathematical relationship
behind phi.
Starting
with 0 and 1, each new number in the series is
simply the sum of the two before it.
0, 1, 1,
2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
The ratio
of each successive pair of numbers in the series
approximates phi (1.618. . .) , as
5 divided by
3 is 1.666..., and 8
divided by 5 is 1.60.
The table
below shows how the ratios of the successive
numbers in the Fibonacci series quickly converge
on Phi. After the 40th number in the series,
the ratio is accurate to 15 decimal places.
1.618033988749895 . . .
|
|
This
ratio has been used by mankind for centuries.
|
|
|