--- In FairfieldLife@yahoogroups.com, off_world_beings <[EMAIL PROTECTED]> wrote: > > --- In FairfieldLife@yahoogroups.com, bob_brigante <no_reply@> > wrote: > > > > --- In FairfieldLife@yahoogroups.com, off_world_beings <no_reply@> > > wrote: > > > > > > It is one of the Fibonacci numbers that relates to the Golden > > Section, > > > a ratio found in an incredible (mind-boggling) number of > situations > > in > > > nature. > > > > > > OffWorld > > > > > > > ************* > > > > http://www.textism.com/bucket/fib.html > > > > Nice. > > One thought is that because the human body has proportions that > include an approximation of the golden section, so from birth we > attune ourselves to that porportion and then find it in nature also, > but that seems too simplistic. You could also say that it has > efficincies that are practical in nature, but then you are saying > that it has some pre-ordained significance, and that would open up a > whole can of worms for some people. > > It also is mathematically related to the number 108, and this > relationship makes it even more interesting: > > ""It could have been otherwise, but it so happens that the distance > between the earth and the sun equals about 108 (actually 107-odd) > times the sun's diameter. Likewise, it so happens that the distance > between the earth and the moon equals about 108 (actually 109-odd) > times the moon's diameter. That sun and moon look equally big in the > earthly sky is the immediate result of their having the same ratio > between distance and diameter. Moreover, it so happens that the > sun's diameter approximately equals 108 times the earth's > diameter...."" > > ...""Can we be sure that this remarkable astronomical state of > affairs has played a role in the selection of 108 as a sacred > number? Did the ancient Indians know about the moon's diameter or > its distance from the earth? According to Richard L. Thompson > (Mysteries of the Sacred Universe, Govardhan Hill Publ. 2000, p.16, > p.76), the medieval Sûrya-Siddhânta gives an unrealistically small > estimate for the distance earth-sun, but the estimate for the > distance earth-moon and the lunar diameter differs less than 10% from > the modern value. The ratio between distance and diameter of the > moon is implicitly given there as 107.5, admittedly a very good > approximation. "" > > ""A conditional geometrical property of 108 is dependent on the > conventional division of the circle into 360°. ..."" > > ""...But for now, we may settle for the division in 360°. In that > case, the angle of 108° has a unique property: the ratio between the > straight line uniting two points at 108° from each other on a > circle's circumference (in effect one of the sides of a 10-pointed > star) and the radius of that circle equals the Golden Section. > Likewise, the inside of every angle of a pentagon measures 108°, and > the pentagon is a veritable embodiment of the Golden Section, e.g. > the ratio between a side of the 5-pointed star and a side of the > pentagon is the Golden Section. So, there is an intimate link > between the number 108 and the Golden Section. But why should this > be important?"" > > ""The Golden Section means a proportion between two magnitudes, the > major and the minor, such that the minor is to the major as the major > is to the whole, i.e. to the sum of minor and major. The general > equation yielding the Golden Section is A/B = (A + B)/A, ... viz. X > equals the limit of the series G/F in which F is any member and G is > the very next member of the Fibonacci series, i.e. the series in > which every member equals the sum of the two preceding members: 1, 1, > 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, This means that every next > fraction G/F, i.e. 1/1, 2/1, 3/2, 5/3, 8/5 etc. forms a better > approximation of the Golden Section, whose value can be approximated > to any desired degree of precision if fractions of sufficiently > highly-placed members of the Fibonacci series are considered."" > > ""In art and architecture, it is found that the Golden > Proportion is naturally pleasing to our inborn tastes. In living > nature, there are plenty of sequences where every member stands to > the preceding member in a Golden Proportion or its derivatives > (square root etc.), e.g. the distances between or the sizes of the > successive twigs growing on a branch, the layers of petals on a > flower, the rings of a conch, the generations of a multiplying rabbit > population, etc. What this symbolizes is the law of invariance: in > every stage of a development, the same pattern repeats itself."" > > http://koenraadelst.bharatvani.org/articles/misc/why108.html > > OffWorld
Very interesting. Fibonacci series, i.e. the series in which every member equals the sum of the two preceding members: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, (notice 34)
