Refinding Phi, Part 2.

 

 
 
 
 
 
 
 
 
 
 
 






The previous post has a Graph whose Pattern reminds me somehow of the Profile of a splash ripple.   I could not discuss further in the last post because the space to do any more not there.
 
There is an old post of mine, "The Tip of a Drop",  in April 2011,  with discussion.

I have always said that there is something funny going on between 0 and 1.
Maybe that is why homeopathy is effective!?  The bucket chemists would not agree.
My feeling is that subtle chemistry and physics is where it is at.   Vacuum energy, etc.
1/0  =  kapow!
It could be that there is a connection with the structure of a torus.  Just guessing.
 I lie awake trying to visualise how it goes, but I do not get pictures
( tho during Primal Therapy in 1975 I did get photographic images!). 
There is a YouTube video describing the Torus
and NassimHaramein has YouTube talks on this subject.
I tried to crochet a torus.......more of this later......
The Sunflower maybe  has the Pattern of a Torus-  all those seeds coming from the centre
and spreading out.....geometry was published 12/12/2012.

There was a lot to say in Post of 12/12/2012, "Our Place in the Universe",  and thereabouts.
The Cosmic Ouroborus".  10 to the Power -33 and all that Planck data.....

Here we go with more Phi data.  My old tables only went to 8 digits on my calculator,  so this is new.
After this Table I will have to go to the next post, Part 3.  Space seems to run out these days....

Refinding Phi, Part 1.

This is a continuation of a similar recent post (5/4/2013)..
The definition of Phi that I know is that
 the Golden Mean or Golden Ratio
is found by calculating
one Fibonacci number divided by the previous Fibonacci number.
That is,  Phi  =  F(n) / F(n-1).
 Let us see what this looks like:-

So far,  they are all a little bit different.  
What is evident is that one Phi = 1 + 1 / another Phi ,  and it is exact.

Moreover,  all can be described in a Graph:-

Internal Structure of Seashells **

Internal spiral is paper thin.

Outer shell can be incredibly thick / strong.

There seems to be protein incorporated with calcium salts.

It feels incredible that the mantle of a sea gastropod is able to engineer so exactly the molecules to create unique structures

These pictures are to correct a pattern made in post of 19/3/2012.

The outside tip of a shell is incredibly hard
and the inside paper thin.

This is important in making models of  work, especially tall thin shells, to avoid bulky crochet inside.










X rays of Seashells


http://www.seashellarchitecture.com
http://shellography.com    The Art of the Ocean by Dr Thad Thomas,  4 galleries incl x rays.
YouTube,  the seashell x ray man, 22 August 2010

Mathematics of Seashells by Xahlee, 2006-05.
The Algorithmic Beauty of Seashells, by HansMeinhardt,Przemyslaw,Prusinkiewics and DeborahRFowler.   from Amazon.....

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Real Seashells **

It is with gratitude for the kind permission of  New Holland Publishing that I can post three pages of real seashell species with their names.  It is easier to imagine how to crochet and knit models of seashells when we have some images to view.

http://www.newholland.com.au

Pictures from "Australian Seashores in Colour" by Keith Gillett and John Yaldwyn,   1968.   

There are a great number of valuable books on the market, describing Seashells worldwide;  eg
"Seashells of SE Australia", by Jansen, soft cover, 414 species, 47 colour plates.

"A Handbook to Australian Seashells", by Dr Barry Wilson


http://www.australianseashells.com.au
http://www.seashells.net.au/seashell_books

The First 135 Fibonacci Numbers ** **

The first 100 numbers are in post of April 16, 2011.
Here  they are again  and 35 more, now that we can calculate large numbers.
I have added them up, and checked them by referring to" the first 300 numbers" published in Dr Ron Knott's website.    http://maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html

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Extra Dimensions

In my young days,  there were 3 dimensions- 
 1.  the dot point,
 2. the flat surface; lines between 2 dots.
 3.  add volume to make 3 dimensions.  All very much Scientific Method.

Early influences were science fiction-  RayBradbury,  Arthur CClarke,  IsaacAsimov.

Then, early 70s,  there were unusual Books.  eg by HermanHesse, CarlosCastaneda.
Then RD Laing and Dr ArthurJanov.  Primal Therapy.
The Conscious, the Subconscious and the Unconscious!
Otherworlds!     Movies were "2001:  A Space Odyssey"

Rebirthing introduced me to Chakras and more mystical realms.
Past Lifetimes came in hypnosis sessions.

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Nowadays it's becoming Cosmic. 

Science Fantasy of TraciHarding and many more writers.

Travelling is in the multi Universe,  most notably by MichaelRoads.

Maths is multidimensional;  Hypercubes!

The Chani Project.   Nexus Magazine is foremost in bringing us new ideas!

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Radio has given us "New Dimensions"  previously from Ukiah, California,
and now fron Santa Rosa, California.  Hosted by MichaelToms and JustineWillisToms,  there have been more than 3000 interview with the best new-thinking minds in America,  a great gift to the world,  and now Stanford University has all interviews archived. 
It is with sadness that I hear of the death of MichaelToms in January 2013.  He will be much missed,  though we can still hear his kind voice and hearty chuckle in re broadcasts.

You can find out more and listen on http://www.newdimensions.org  and http://www.abc.net.au/rn/newdimensions    

---------------no doubt there will be more thoughts on the subject as time goes on....

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Refinding Phi - Introduction

Now that we have a new Calculator at http://web2.0calc.com  I'd like to have a look at Phi with maximum decimal places.  Just checking;  just curious.  Going back to first principles.





****************more work is in progress.  Part 1 is posted 13/6/2013.

Addition to Introduction.   7/7/2013

Please look at the basic data in Wikipedia and on Dr Ron Knott’s website re Phi.

It involves a quadratic equation containing  the square root of 5 .   I don’t know why this has been chosen.

∅² = ∅ + 1 is the equation.

Dr Knott describes how mathematicians have calculated Phi to 1500,000,000 places.  Then in 1996 it was done to 10 million places.  The record was in 2008 to 10,000 million places.  He noted which program was used and how long it took.  I shall not repeat that information here in this little blog.   Please have a look at his Silver Series. And Lucas Numbers.  Amazing.

Also see http://www.goldennumber.net for much info on Phi. 

Particularly check out ELFRAD.

 I prefer to study it all in my own simple way.