Golden Mean ratio
The science of sacred geometry includes study of the Platonic solids, numbers, and the golden mean ratio.. This is all mathematics, and is very interesting if you are so inclined (left brain stuff).
The Golden Rectangle can be drawn using a straight line and compass. It is based on the square root of 5, and is particularly pleasing to the eye. This rectangle was used in some of Leornado da Vinci’s works (eg Virgin in the Cave). Also shown below are two intersecting circles with the Vesica Pisces, and how the three fundamental geometries based on 
, 
and 
are derived from it.
Fibonacci Sequences and the Phi Ratio
The Phi (F ) ratio turns up frequently in nature. It can be derived from geometry or from a Fibonacci sequence. From geometry it’s value is: 
From the Fibonacci sequence (each term is derived from adding the previous two terms):
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, …
diving two successive terms yield values closer and closer to F , eg 10946/6765 = 1.618033999…
Another sequence:
1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, …
yields in the limit when a term from the second series is divided by a term from the first, eg the 18th terms 5778/2584 = 2.236068112… (cf 2.236067978…).
Reciprocal of 89
The reciprocal of 89 is also an interesting number. A calculator will show 1/89 = 0.011235955… A bit of programming (I did it in Visual Basic on Excel) will show that it is a recurring decimal with 44 decimal places:
0.01123595505617977528089887640449438202247191 011235955 etc
The unique book on Vedic mathematics (by Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja, Sankaracharya of Puri) describes how to deal with reciprocals of this type, in this case the Ekadhika is 9 and the last term of the recurring decimal is 1. Only the first 22 terms need by derived by multiplication by 9 (the Ekadhika) at which point 88 (which is the denominator minus the numerator) is obtained. The rest of the terms are derived by 9’s complement, ie:
9887640449438202247191
0112359550561797752808
----------------------
9999999999999999999999
Starting from the top right, 1 x 9 = 9, which is the 2nd digit. 9 x 9 = 81, put down 1 carry 8. 9 x 1 = 9 + 8 = 17, put down 7 carry 1, etc.
Just thought I’d mention that for fun! The Fibonacci sequence is actually "hidden" inside 1/89, viz:
0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 . .
1 2 3 5 8 4 3 7 1 8 9 8 8 6 4 1 5 6 . .
1 2 3 6 9 5 5 1 7 9 7 6 3 . .
1 2 4 6 0 7 8 6 . .
1 1 2 4 . . .
0 1 1 2 3 5 9 5 5 0 5 6 1 7 9 7 7 5|2 8 0 0 0 3 8 …
On the top line I have started to write the Fibonacci sequence, 1, 1, 2, 3, 5, 8, 13. At 13 I put the 3 on the top line and carry the 1, adding it to the 8. This continues carrying 12 when we get to 123, etc. There are also 1's which get carried when the columns are added together. The | shows the accuracy of 1/89 for the number of terms of the Fibonacci sequence taken - when the numbers are all added up you get 1/89. The significance of the 44 recurring decimals is interesting as it is the number of chromosomes in the human body (44 + XX or XY) - is this just a coincidence?
© In the Light, 18 March, 2011 , Disclaimer, Son of Suckerfish drop-downs from HTML dog