biology and geometry

RECREATIONAL MORPHOMETRY

Klly

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This blog consists of two sections (two entries , both started at 2008). The blog is updated about once a week .

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MOTIVATION

To attempt the most simple geometric look we have choosen only a few values .Actually be reduced to only three : g , j and d .

STARTING VALUES . (Values g and j )

SERIES 255 = (1+2+4+8+16+32+64+128)

The series 255 can be identified with the following items : breath , sigh , blow , run ,action ...

{ We have found an interesting article in wich an image called our attention :

''A quantitative analysis of the mecanism that controls body size in Manduca sexta '' HF. Nijhout et al. Journal of Biology 2006 , 5 : 16 Pay attention to the image 3b where we see a very illustrative image of the concepts mentioned above . }

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Another one series frequently used in this blog : series ( 1+1/2+1/16+1/32 ) and
series 51 = ( 32+16+2+1 ) :

                                                                  series   51

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On the road , combining g and j  with the series (1+1/2+1/16+1/32) we performed one pretty good approximation to ' Pi ' .

RIGHT TRIANGLE IN WICH THE SUM OF THE LEGS IS CLOSE TO Pi .

According to that we have this depiction :

                                        WAYS TO DRAW Pi .



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There are two concepts related to the matter developed in this page :

1 . FRACTAL : structure that has the same appearence at different scale
2 . ACTION     : an atribute of a physical system product of the energy and duration of a process .

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Will to see recreational relationship among Starting values described previously .
Take a look at the following relation among Pi , ( g + j ) and amino acid Glycine . Glicine is the smallest of the 20 amino acids commonly found in proteins .Glycine is coded for by the codon sequences GGU , GGA , GGC , and GGG . Instead of codon , will see relations between amino acid - anticodon . So that Glycine anticodons are : CCA , CCU , CCG and CCC .

Glicine molar mass : [5705]
Cytosine molar mass : [1111]

It's worth to say that we're using significant digits only :

GLYCINE ANTICODON

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BIOELEMENTS .

Most of biomolecules are made of Hydrogen , Carbon , Oxygen and Nitrogen .
Using the Starting values such as Pi , the series 51 = (32+16+2+1) and ( g + j ) :

BIOELEMENTS GEOMETRY .

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WATER AND CARBON .

Molar mass of the Water : [18,0156]

Atomic mass of Carbon : [ 12 ]

WATER , CARBON AND THE SERIES 51 .

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SOME GEOMETRIC OBSERVATIONS IN BIOLOGY .

Now , we will use the series ''255''=(1+2+4+8+16+32+64+128) as follow :

SERIES OF 22 ELEMENTS . According to an economy's principle : (1+2+4+8+4+2+1 )
wich remember a palindromic (symetrical) sequence .We call nymph sequence :

                                                           NYMPH   SEQUENCE .

The  Vulva of Caenorhabditis elegans worm consists of 22 cells . that is , 1+2+4+(8)+4+2+1
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Micro RNAs shows typically an average of 22 nucleotids in length .

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Insulin preproprotein in Homo sapiens has 110 amino acid in length

Insulin 2 preproprotein of Mus musculus has 110 amino acid in length

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Mioglobin molecule of many species has 154 a.a. = 7(22)

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Disacharides such as sucrose and lactose have 22 atoms of hydrogen

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Human mitochondrion encodes 22 t-RNA , required for mitochondrial protein synthesis .

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HUMAN SKULL consists of 22 bones =

the cranium bones : occipital , two parietals , frontal , two temporals , sphenoidal , ethmoidal .

the skeleton of the face : two nasals , two maxillae , two lacrimals , two zigomatics , two palatines , two inferior nasal conchae , vomer , mandible .

VERTEBRAL COLUMN is formed of a series of 33 vertebrae ( 22 + 11 ) :

seven in the cervical region , twelve in the thoracic , five in the lumbar , five fixed in the sacral , and four fixed in the coccygeal .

THE BONES OF THE LOWER EXTREMITY

The hip bone : Ilion , Isquion and Pubis (wich are distinct each to other in the young subject)
Then we have : Femur , Tibia , Patella , Fibula
The bones of the foot : Calcaneus , Talus , cuboid , Navicular , and the first , second and third Cuneiforms .
The Metatarsus consists of five bones .
The phalanges of the foot are two in the great Toe and three in each of the other toes .
   So that the sum results  33 bones .

[ Source : ''Grey's Anatomy of the Human body '' ]

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Green plants need to live and grow the molecule of carbon dioxide (CO2) .

The sum total of atomic number of chemical elements involved is equal to 22 : C-6 , O-8 .

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Most of Amino acids are made of carbon , hydrogen , oxygen and nytrogen .

the sum of atomic numbers is :( C-6) +( H-1)+(O-8)+(N-7 )= 22

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Nucleic acids , DNA and RNAs are made of carbon , hydrogen ,oxygen , nytrogen and phosphorus . atomic number of phosphorus is 15 .

so that we apply here a combination or sum of series 22 +15 .

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Dental formula of the ancestral placental mammal is :

I-3/3 , C-1/1 , P-4/4 , M-3/3 . The total are equal to 44 .

Dental formula in Human species (adult) is : 16 teeth in the upper jaw and 16 in the lower jaw .

Using our recreational form we will write as follow :

(1)+(2)+(4)+(8)+(4)+(2)+(1) where numbers coloured in orange has been removed .

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SETS   OF   THINGS   .

Will to apply the series 51=(32+16+2+1) in such a way that exhibits symmetrical appearance :

Say (32+16+2+1+2+16+32) . We call butterfly sequence :

BUTTERFLY SEQUENCE .

For instance , the worm Caenorhabditis elegans has (when adult) 959 cells . Applying
the series 51 we've performed the following depiction :