New Seashells.

More images of seashells given to my by Penny.

Murex  (2 varieties)    Now these might need the Equation involving Number 9,  or 18,  which was discovered quite a while ago, on this blog.......one day we will try it........

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

Some great specimens found in an old secondhand shop in Old Bathurst Rd, Katoomba, in the Blue Mountains west of Sydney.

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

This one is a Conus.

This is also a Conus.










There is a Story     -  There was a time when  certain rare Seashells were very much prized and sold for huge sums of money.  One shell was Conus Gloria Maris  -it looks much like the first one.  They thought it was rare,  Chinesec craftsmen made fakes out of paper and fooled many a collector....until there were many real shells found in an area of sea near the Phillipines.

One can find a list online of historical Personages who collected seashells.  One is Fidel Castro who can dive and find his own in the pristine Coral Reefs around Cuba.  A poor country,  Cuba was forced to grow food organically because it was impossible to buy fertiliser---- thus the reefs are not damaged.  Wonderful.  We can Learn from Cuba.  There are Staghorn Corals there which now occur nowhere else.  The worry is that Cubans might take on Western methods--- and thereby lose their hard won assets of Marine Life........officialdom has much to answer for.
You can see a YouTube video of Cuba's coral reefs (Accidental Eden)  shared on this very blog in previous post---
----------------------------------------------------------------------------

The Operculum of a Gastropod. And the Abalone.

At the beach, Little Bay, in Sydney,  I found some pieces from seashells, namely the operculum, the door which the animal uses to open and shut its opening.  It has the mark of a perfect SPIRAL.
The idea is to study how to make a model of this and to elucidate the Numbers!

1.  a drawing,  and the real thing, next.
Size may be 2 cm or so.

2. the underside,  which would  have strong muscles from the mollusc's mantle attached to it.

3.  the outside of the operculum,   and a crochet hyperbolic fibonacci fan-----one can see how it naturally configures its shape just so....  more images to follow.....

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

4.  A Real Abalone seashell with pearly inside,  nacre,   which is said to be made of Calcium minerals and a protein, lustrin.

5.  The outside of the abalone shell has red coral growing on it!  And little barnacles, and a tube worm with hard case, like Galeolaria maybe.  You can see the outer rim has spiracles, respiratory holes.    One day we might be able to discover how to make a model of this Shell.

Wonderful Oceania!   One can only marvel and admire.


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

Table for the Half Fibonacci Series and the Algorithm 4 to 5 Series.

n	Fib n and Fib n 1/2	Alg 4 to 5
0	0
	½
1	1
2	1
2 ½	1 ½
3	2
3 ½	2 ½
4	3	4
4 ½	4	5
5	5	7
5 ½	6 ½	6
6	8	8
6 ½	10 ½	10
7	13	12
7 ½	17	15
8	21	18
8 ½	27 ½	22, 27
9	34	33
9 ½	44 ½	41
10	55	51
10 ½	72	63
11	89	78
11 ½	116 ½	97
12	144	121
12 ½	188 ½	151, 188
13	233	235
13 ½	305	293
14	377	366
14 ½	493 ½	457
15	610	571
15 ½	798 ½	713
16	987	891
16 ½	1292	1113
17	1597	1391
17 ½	2090 ½	1738, 2172
18	2584	2715
18 ½	3382 ½	3430
19	4181	4287
19 ½	5473	5358
20	6765	6697
20 ½	8855 ½	8371
21	10946	10463
		13078
22	17711	16347

Note:

Fib n ½ = 1/2 Fib( n + 2)

Eg F 19 ½ = ½ F 21

5473 = ½ 10946

F16½ = 1292 = ½ F18

= ½ x 2584

F18 ½ = 3382 ½

= ½ x F20 = ½ x 6765

F8½ = ½ F10

=27½ = ½ x 55

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

Fn½ - Fn = F(n-2½)

F18½ - F18 = F15½?

3382.5 – 2584 = 798.5

 = yes

F15½ -F15 = F12½

798½ - 610 = 188½

=yes

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

OK  This is how it looks when it is typed with table grid on Word Document, then copied (control c) and pasted (control v)  onto blog post.

Maybe this is better than my handwritten Tables....

There are interesting new equations and equivalences here...some are as just above.

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

One can see that the 4 to 5 series follows the half Fibonacci series to some small degree,  but numbers begin to diverge widely as the Series ascends.

I have previously worked out how to micro adjust  numbers at the end of the crochet  or knit work to exactly follow the Fib and a half Series
 see 9/13/14 ie 13th Sept 2014 for 3 tables describing
progress visually, like a map.
******************************************
Next I can give you a map of how the 4 to 5 Series grows...   as soon as the diagrams are drawn........

1/8/2017    ***Column 3 on this post. shows how the 4 to 5 series grows
--------------------------------------