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

Now that we have a new Calculator at http://www.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 will follow asap.

Kind Advice.

The universe gives us answers if we work towards it!
At the end of a recent post, Phi Furthermore, 1/3/2013, I was remarking on how one gets different answers to calculations, depending on how many decimal places one uses.  My calculator only has 8 digits, so my work is limited.
I emailed a real mathematician who understands Fibonacci Series and he most kindly replied.
I am very grateful for it has opened up a new way for me.
Here is part of his reply:-

My Phi to the power 36 was 33385270  and this is close, but not exact.
maybe I should write "33385270........." to be more honest.
For my own purposes it is ok to be not too exact for one can see Patterns and Equations to show Rules or Trends.  I am glad to offer these distinctions in the interests of better reporting.

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This is more advice for me to work with.  This is the second time a mathematician has mentioned the Lucas Series to me,  but only now do I understand.

 

If Phi to the power 36 is 33385281.999999900466810494516.....

then Phi to the power minus 36 , ie 1 / Phi to power 36 = 

 0.0000000299533189505484

using the Scientific Calculator.

Adding them together  =  33385282

which is the nearest integer!

= A whole new world.

 

 

My thanks the the mathematician who gave me good advice. 

 I welcome comments anytime, especially if I have made some mistake, (which often happens).

 

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I searched online for Mathematica or similar to enable me to do long calculations.

I founs it to be a software program from Wolfram Maths, and it costs more than $100.

A cheaper one was Math Studio which I purchased for $30.  When I looked into it,  yikes it was forbiddingly complicated!  More difficult than my first year university maths in 1966!

  I clicked on fibonacci - and foiled already!-    "file unknown".  All I wanted was a better calculator.

 

Next try was looking for an online calculator and I found a Free one.

http://web2.0calc.com    This is a Scientific Calculator and it works to 50 digits or so.

 

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There is more story.......... When I looked for www.mathstudio.net I was WARNED security problem with this site!  I felt a bit cheated and worried. 

 I tried http://www.mathstudio.net and this one was OK.

 

(PS. 10/5/2013  The professional computer repairers at Propellerhead fixed it for me,

 icon, maths file and all.  Thanks, guys.)

 

It was a big lesson for me. 

All the online references I quote in my blogs should have http:// in front of them for the security of my readers! 

Yikes--- what a big job if I have to go and correct all my  work!  Plus correcting all my numbers.

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It has been a long hot and dry Summer in my caravan without electricity. Hardly any rain.  Not much luck growing vegetables.  Hardly any bees.  Fire! 8 km away, twice, east and south.   I will post photos in my other blog asap.  Autumn is bringing kinder days and hopefully a Happy Easter.

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Diorama with Mermaid and Seashells

As promised,  I got it together,  but the wind blew it all over the place when I was taking the photo.
I was  a bit frazzled,  so it is as it is.  One day things might be more perfect....

 

 

 

Please see May 25, 2010 post "Instructions for Making a Model of a Seashell". 

There is  a lot of information in the early pages of this blog. 

 More work will be done in future to perfect the spiral at the tip of seashells.

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