Phi in nature
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From: Jimmy on 8 Sep 2005 05:31 What is so special with Phi? What does it mean? In an overwhelming number of plants, a given branch or leaf will grow out of the stem approximately 137.5 degrees around the stem relative to the prior branch. In other words, after a branch grows out of the plant, the plant grows up some amount and then sends out another branch rotated 137.5 degrees relative to the direction that the first branch grew out of. All plants use a constant amount of rotation in this way, although not all plants use 137.5 degrees. However, it is believed that the majority of all plants make use of either the 137.5 degree rotation or a rotation very close to it as the core number in their leaf or branch dispersion, sending out each and every leaf or branch after rotating 137.5 degrees around the stem relative to the prior branch. If we were to multiply the value of 1 over Phi to the second power (0.3819659.) times the total number of degrees in a circle (360), we obtain for a product nothing other than 137.50. degrees. As an alternate way to look at the same idea, if we were to take the value of 1 over Phi (0.6180339) and multiply it by 360, we obtain approximately 222.5 degrees. If we then subtract 222.5 from 360 we again find 137.5 degrees - in other words, the complimentary angle to 1 over Phi is 137.5 degrees, which also happens to be the value of 1 over Phi to the second power times 360. So, if we have followed the described mathematics, it is clear that any plant that employs a 137.5 degree rotation in the dispersion of its leaves or branches is using a Phi value intrinsically in its very form. Considering our discussion in the prior section on Phi in geometry, it is interesting to note the off-balance five-pointed star that can be seen in the leaf pattern of plants that employ a 137.5 rotation scheme when they are viewed from above.
From: Andy Resnick on 8 Sep 2005 08:29 Jimmy wrote: > What is so special with Phi? What does it mean? > <snip> The golden mean/golden ratio, denoted by the Greek letter Phi, represents the ratio between two parts such that the whole is to the larger as the larger is to the smaller. Why this is pleasing, I do not know. Nevertheless, objects made using Phi as a parameter appear to be 'designed' or more 'rational' than not. -- Andrew Resnick, Ph.D. Department of Physiology and Biophysics Case Western Reserve University
From: Schoenfeld on 8 Sep 2005 09:26 Jimmy wrote: > What is so special with Phi? What does it mean? It is the only number with the recurrence relation: phi^n = phi^(n-2) + phi^(n-1) That is why it is such a special number. The rest are details.
From: Jimmy on 8 Sep 2005 09:54 "Andy Resnick" <andy.resnick(a)op.case.edu> wrote in message news:dfparr$gjs$1(a)eeyore.INS.cwru.edu... > Jimmy wrote: > > What is so special with Phi? What does it mean? > > > <snip> > > The golden mean/golden ratio, denoted by the Greek letter Phi, > represents the ratio between two parts such that the whole is to the > larger as the larger is to the smaller. Why this is pleasing, I do not > know. Nevertheless, objects made using Phi as a parameter appear to be > 'designed' or more 'rational' than not. > -- > Andrew Resnick, Ph.D. > Department of Physiology and Biophysics > Case Western Reserve University I just read On Dan Winters site that when we have the feeling of love or compassion Phi can be found within the ekg. He says itýs self awarness because of the nature of waves...something :) Earth can become self aware if the energy (Szhuman??) resonate with Phi, he says.
From: PD on 8 Sep 2005 11:03
Andy Resnick wrote: > Jimmy wrote: > > What is so special with Phi? What does it mean? > > > <snip> > > The golden mean/golden ratio, denoted by the Greek letter Phi, > represents the ratio between two parts such that the whole is to the > larger as the larger is to the smaller. Why this is pleasing, I do not > know. Nevertheless, objects made using Phi as a parameter appear to be > 'designed' or more 'rational' than not. > -- > Andrew Resnick, Ph.D. > Department of Physiology and Biophysics > Case Western Reserve University This is a basic fractal behavior. What this indicates is that nature likes to grow things fractally. Note that fractals exhibit not only self-similarity but also suprising complexity from a minimum number of rules. This is why Wolfram finds cellular automata so interesting, and why MIT's robotics group (Rodney Brooks) has been busy *reducing* the intelligence of its robo-insects' leg actuators with remarkable success. PD |