Wednesday, April 19, 2017

Mathematical Impressions: Shell Games

"Mathematical Impressions: Shell Games"

There is a YouTube video  of this name.  I tried to share it.....
but was unable.
it is by Simons Foundation.   Rules for complex designs on Cone shells!

Rule = make a line of light and dark shells in a row.
Put a white shell under the middle shell of any 3 of the same colour in the row.
Put a dark shell under the other shells.
Continue.

Tuesday, April 18, 2017

Fibonacci Poetry

Yes!  Poetry in accordance with the Fibonacci Sequence!

Wordsworth did it:-
I wander'd
lonely as a cloud
that floats on high o'er hill and vale
and all at
once I saw a crowd
a host of golden daffodils
3, 5, 8;  3, 5, 8;
Only kidding.  It is 8, 8, 8, 8, .

Amazon has e-book by Virginia Gow.  "Escarpment".
I used to live in the Blue Mountains, west of Sydney,
and I can relate to the landscape.  I love it.  And I love Virginia"s poetry.

There is more online on the subject.
I am just posting this to show I am still here.
Today I posted myLetter on www.awhatifworld.blogspot.com.
There is a lot to think about.
And I am still working on my seashell maths.
May all be well.

Thursday, December 22, 2016

Christmas tree

It has been traditional for me to feature some Christmas item each year.
Remember we used to roll up a newspaper, cut from top to halfway down all layers, and then pull out the inner tip - to make a tree?

Like so:-

from strips of paper of fibonacci lengths, I wondered how many spirals up there were as we increase the length of paper:-


This might help in elucidating a method to crochet seashells with tall spires.
.....................................

This next is my best work done this year:-

This is Fibonacci series made in a flat spiral.  It works out as a 6 1/2 sided polygon, with crests.  I published the earlier work to 233 stitches perimeter in Post of ...24/12/2015....
This one is 377.   All the mathematics is in  previous post mentioned.
You need to click on images to enlarge them.
Then right click and you can save, or download, to print out Pattern, if you so desire.

38  rows more and we could have 610, but I will not attempt it.

......................
here is a model of striped seashell, not yet perfected....
from this:-


The real things:-


.........................


My new solar system.  One panel on the roof;  inverter;  12 volt;  I can charge up my mobile phone etc  but we still do not have internet or proper mobile phone reception in our town!  I am typing this in IGA , seated in cool area, before catching taxi home to my caravan out of town.  That is why so few posts.....Better luck next year. 
Happy Christmas everybody.
....................................

Sunday, October 9, 2016

Biomathcraft Index, from the Beginning in 2010.

BIOMATHCRAFT INDEX

------------------------2010------------------
1.        How to create models from Nature.    3/30/10
2.        How to crochet a Hyperbolic Seashell.                        4/29/10
3.        Fibonacci Series Pattern.             5/19/10
4.        Instructions for Making a Model of a Mollusc.          5/25/10
5.        Photogallery of Seashells, crocheted and knitted.   5/25/10
6.        More Seashell Gallery.      5/25/10
7.        Photo Gallery of all my Seashells so far.          5/25/10
8.        Variations on a Hyperbolic Theme.       5/26/10
9.        How did I begin this Adventure?           5/26/10
10.      Hyperbolic Crochet on Radio.    5/26/10
11.      Who was Fibonacci?         5/26/10
12.      Unpacking the Fibonacci Series and the First Model.          6/21/10
13.      Here are the Bivalves.       6/23/10
14.      Heterodontus does Crochet.      6/24/10
            The Bifurcating Series.      6/24/10
            Heteronympha Fluttered By.      6/24/10
            An Important Message.    6/28/10
            One Big Family.  Ancestors!      8/15/10
15.      Fibonacci Equations.         11/21/10
16.      Fibonacci Series;  Mistakes.         12/5/10
17.      More Series, and IFF.        12/20/10
18.      A Theoretical Fibonacci Christmas Tree.          12/21/10
------------------------2011---------------------
19.      Fibonacci Series Table of First 100 Numbers.            4/16/11
20.      Fibonacci Cones, Type 1. 4/16/11
21.      Fibonacci Cones, Type 2. 4/17/11
22.      “Fibonacci Ripples”, Type 1.       4/17/11
23.      “Fibonacci Ripples”, Type 2.       4/21/11
24.      The Tip of a Drop.  4/21/11
25.      Beyond Zero.           4/21/11
26.      Make a “Fibonacci Pyramid”.     4/24/11
27.      Giza Pyramid.          4/24/11
28.      Imaginary Giza-Like Fibonacci Pyramids.        4/24/11
29.      Our Solar System.  4/24/11
30.      Crafting the Vortex:   the Beginning.    4/28/11
31.      More Crocheting the Vortex.      4/28/11
32.      Pattern 1 for “Fibonacci Vortex” to 233.        4/28/11
33.      Pattern 2 for Vortex to 4181.     4/28/11
34.      Pattern 3 for Imaginary Vortex to 196418.   4/28/11
35.      Discussion on Pyramids.  5/2/11
36.      Horns, Tusks, Fangs and Thorns, Spines and Prickles.         5/3/11
37.      Equations for a Frilly Edge.          5/3/11
38.      Tribute to Helle.      5/3/11
39.      To Crochet a Cephalopod.           5/3/11
40.      More Molluscs.       5/25/11
41.      New Models of Snails, made last year…          5/26/11
42.      The Giant Clam!      5/26/11
43.      More on the Bivalves.       5/26/11
44.      Real Seashells.         5/26/11
45.      “Fibonacci Bivalve Equations”    5/26/11
46.      Fibonacci Equations Having the Number 9.   6/5/11
47.      It looks like a Clam…          6/16/11
48.      Australian Seashores,  Identification of Shells.         
49.      Playing With the Number 9.       6/16/11
50.      Parallel Universes. 7/20/11
51.      Time Flies!    11/22/11
------------------------2012-------------------------
52.      A Proper Pattern for a Fibonacci Seashell.     1/19/12
53.      Make some New Fibonacci Seashells. 
54.      Now it’s Getting Closer to the Real Thing!       2/24/12
55.      The Seashell Model for 2012.     2/24/12
56.      On  the Trail of the Fibonacci Snail.      19/3/12
57, 58.                       Tribute to Tom Bass.
59, 60.           Tribute to Trudy.    19/4/12
61.      A Small Model, and a cute mermaid.   6/13/12
62.      More Mermaids.    8/1/12
63.      Visuals for Fibonacci Series.        8/1/12
64.      Errors Galore! And a Beautiful Solution.         10/25/12
65.      Responding Literally.         12/12/12
66.      Our Place in the Universe.           12/12/12
67.      Powers of Pi.           12/12/12
68.      Mending Mistake # 1.       12/12/12
69.      Powers of Phi.         12/12/12
70.      Powers of Further Phi.     12/12/12
71.      Geometry of a Theoretical Sunflower.            12/12/12
72.      Real Sunflowers.    12/17/12
-----------------------2013--------------------
73.      Angles for Fibonacci Series, 137.5 degrees.   1/7/13
74.      Angles for Sunflowers.     1/7/13
75.      Angles for Giza Pyramid. 1/7/13
76.      More Data, on angles, and Phi(s).         1/7/13
77.      “The Whole Bang Lot”.     1/7/13
78.      Planck and Phi.       1/7/13
79.      Continuing from last posts…..     1/31/13
80.      Phi Furthermore.   1/31/13
81.      Mathematics at Large.      1/31/13
82.      The Vedic Connection.      1/31/13
83.      Diorama with Mermaid and Seashells .           1/31/13
84.      Kind Advice.             3/25/13
85.      Refinding Phi – Introduction.     5/4/13
86.      Extra Dimensions.  5/4/13
87.      The First 135 Fibonacci Numbers.         5/4/13
88.      Real Seashells.         5/4/13
89.      Internal Structure of Seashells.  5/4/13
90.      Refinding Phi, Part 1.        Anatomy of Phi.     6/13/13
91.      Refinding Phi, Part 2.        6/13/13
92.      Refinding Phi, Part 3,        6/13/13
93.      Refinding Phi, Part 4, The Giza Pyramid.         6/13/13
94.      The New Parliament House, Canberra, Australia.  A Temple Pyramid!  8/23/13
95.      My Summary of Fibonacci-type Series and Phi-type Series.         8/23/13
96.      Phi and the Square Root of 5.    8/23/13
97.      Playing With Pythagoras.            11/26/13
98.      Fibonacci Spirals.   11/26/13
99.      A Shaman Mentions the Fibonacci Series.      11/26/13
100.   Proportional Calipers.       11/26/13
---------------------------2014------------------------
101.   A Late Christmas.   11/6/14
102.   A Brand New Calendar!    2/1/14
103.   Adding Time and Spce to Seashell  Models.    2/1/14
105.   The Torus.    2/5/14
106.   The Human Torus. 4/16/14
107.   The Latest Seashell Model.          4/16/14
108.   Swirling Shapes.     4/16/14
109.   Are the Robots Waking Up?        4/17/14
110.   Closer to a Better Pattern.**      5/19/14
111.   A Paper Model.**              7/31/14
112.   Some People and the Models They Make.**             8/22/14
113.   The Yellow and White Model.**           8/22/14
114.   The 144 Model, Crocheted.**   9/12/14
115.   Review of Algorithmn 13 to 21 for Fibonacci Series Crochet and Knit Work.**         9/13/14
116.   A New Equation!    Fibonacci and Lucas Numbers.  9/13/14
117.   Rummaging Around in an Equation.    9/13/14
118.   Combining the Fibonacci Series and the Half Fibonacci Series.**           9/13/14
119.VIDEO.  (OfficialMovie) THRIVE:  What on Earth Will it Take?
120.VIDEO.  Pi The Torus and Consciousness.  Arthur Young.      9/25/14
121.VIDEO.  A Stunning New Map Reveals For the First Time Where Our Galaxy Fits Into……9/25/14
122.   A Discussion of the Torus.           9/26/14
123.   An Hyperbolic Crochet Torus.**           9/26/14
124.   A Hyperbolic Crochet Apple.** 9/26/14
125.   a Rainbow Torus, Algorithm 9.**         9/26/14
126.   A Hyperbolic Crochet Donut (Torus).**          10/7/14
127.   A Golden Ring, Crocheted.**     10/7/14
128.VIDEO.  Science to Inform Conservation – Ningaloo Marine Park. 10/1116/14
129.   More Models – Hyperbolic Crochet Spheres etc **            10/19/14
130.VIDEO.  Bead Crochet Demo – Seven Colour Torus in Pony Beads..           12/6/14
131.VIDEO.  How to Crochet With Beads.** 12/7/14
132VIDEO.   The 4 & 7 Colour Mapping of Reality.  Arthur Young.         12/7/14
133.   A Red Blood Cell, Crocheted.**12/7/14
134.   A Fibonacci Christmas Tree-  Crocheted Cone.**     12/7/14
135.   Information for US and UK Crocheters.**     12/26/14
136.   Beach and Rock Platform, Little Bay, Sydney.           12/28/14
---------------------------2015----------------------------
137.VIDEO.  Soft Coral Habitiats in the Port Stevens-Great Lakes Marine Park.         1/25/15
138.   Crochet Coral Reef:  The Book    1/25/15
139.VIDEO.  Soft Corals Inside the Ex-HMAS Brisbane, -September 2010        1/25/15
140.VIDEO.  Heron Island Coral Reef.  1/26/15
141.VIDEO.  Conserving Cuba’s Coral Reefs.  1/26/15
142.   Fibonacci Ripples Merge into a Spiral.**        1/26/15
143.   Mathematical Model for a Seashell with a Tall Spire.**     2/11/15
144.   Auger Shell  with Tall Spire, model making continued…**                        2/11/15
145.   The Seashell Models Continue.** tall pointy             3/10/15
146.   Seashell Models.**            3/20/15
147.   A Gallery of Seashell Models.**            4/2/15
148.   A New Knitted Seashell**            4/2/15
149.   Nature Spirits!         4/2/15
150.   Making a Pink Seashell.**           4/15/15
151.   Blog Problems.        4/23/15
152.   Making a Pink Seashell, Part 2.**         6/3/15
153.   Making a Pink Seashell, Part 3.**         6/11/15
154.   A Pink Seashell, Part 4.**            7/4/15
155.Table For the HALF Fibonacci Series and the Algorithm 4 to 5 Series.       9/18/15
156.   The Operculum of a Gastropod.  And the Abalone. 9/18/15
157.   New Seashells.        9/18/15
158.   The Body of a Gastropod.            10/1/15
159.   Some Eternal Protocols for Building one Fibonacci Number into the Next, part 1.    11/9/15
160.   An Eternal Protocol, Part 2.        11/19/15
161.   Eternal Protocol, part 2, continued.     11/22/15
162.   Eternal Protocol, Part 3.  11/22/15
163.   Eternal Protocol, part 4.  The 3, 6, 9, etc        12/17/15
164.   Eternal Protocol, Part 5.  Prime Numbers.     12/17/15
165.   Eternal Protocol for Building Numbers;  Summary! 12/17/15
166.   Theoretical Fibonacci Ripples IAW the Protocols.     12/24/15
167.   Christmas Baubles.            12/24/15
168.   Theoretical Fibonacci Vortex Christmas Tree.**       12/24/15
---------------------------2016-------------------
169.   Variation on Ripples,  and 7920.           1/29/16
170.   The Holy City, New Jerusalem,  and 7920.     3/14/16
171.   To Make a Multi-Sided Polygon.**       3/14/16       
           


                                    

Saturday, August 20, 2016

More is Yet to Come

My last post was April 11 2016;   now it is August 21 2016.

There is more work to come, using an equation with No. 18;  for vertical stripe or knob seashells.

Plus more....

1/9/2016
I corrected a mistake in the Holy City, a previous post.....
12000 furlongs is 1500 miles, not 15000 miles....!

******************

Monday, April 11, 2016

Circle with Vertical Stripes







This will be useful when I make a seashell model with vertical stripes, spines or processes.
More work to follow.

Very soon I will have some solar electricity, after 14 years of living in a caravan without.  One hopes that a more orderly presentation of my blog's work will be a result.  Thank you people for your interest over the years.

-------------------------------------------------

Monday, March 14, 2016

To Make a Multi-Sided Polygon.

This is not Fibonacci numbers.  It is Algorithm 6 to 12.


It could be a good Pattern for a baby blanket, made in 2 ply baby wool,  but we are unable to buy this any longer in our town.  One has to go to Canberra or Sydney or online to buy fine wool.  And this in a country full of sheep!

I got up to 192 stitches and then I ran out of wool.....  I mark each increase row to keep track....









This is mind map of Pattern.
Please click on image to enlarge, or right click to download or save.

 Increase 6 stitches each row 6 times.
Then 6 stitches each row 6 x.
then 12 stitches every second row 6 x.
Then 24 stitches every 4th row 6 x. .........
then 48 stitches every 8th row, 6 x.  etc as per next Table



At 48 rows we have a 24 sided polygon with 288 stitches at circumference,  going on to the next set, a 48 sided polygon....etc...as per next Table.



















I begin with 6 chains, join them and do 6 single crochet,  then continue in spiral, marking end of row with a darker thread eg black.  
Then 6 to 12 ( crochet 2x in each loop.)
Then 12 to 18 ( crochet 2x in every 2nd loop).
Then 18 to 24 ( crochet 2x every 3rd loop ie 3 to 4).
Then 24 to 30 (crochet 2x in every 4th loop ie 4 to 5).
Then 30 to 36 (crochet 2x in every 5th loop ie 5 to 6.)...........36 st. Hexagon.
All 6 x.

A 12 sided polygon at 144 stitches.
please click on image to enlarge it.  right click to download or save.


I have included larger numbers just as an academic exercise to describe the ongoing principles.



***there is more info to add asap.