-- Pi inside me ?

viernes, 21 de noviembre de 2008



RECREATIONAL MORPHOMETRY



                                           Klly                                                                       


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

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

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


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 . }

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

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

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  .

                         

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

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 .

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

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

------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------
 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  .


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

WATER AND CARBON .

Molar mass of the  Water : [18,0156]

Atomic mass of  Carbon : [ 12 ]


                                      WATER , CARBON AND THE SERIES  51  .

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



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


  Micro RNAs shows typically an average of 22 nucleotids in length .

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


Insulin preproprotein in Homo sapiens has 110 amino acid in length

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

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


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

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


Disacharides such as sucrose and lactose have 22 atoms of hydrogen

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

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

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



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 '' ]

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

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 .

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

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

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

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 .

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

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 .

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


 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 :


                                                          C. ELEGANS   CELLS  .


    Nervous  system  consists  of  302 Neurons
Here you can play with this subject :



                                                        C . ELEGANS  NEURONS  .
 

( source WORMATLAS  )

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




 
                               


                                                

































































































































































































































































































































Licencia Creative Commons Biology and geometry por A . Coe se encuentra bajo una Licencia Creative Commons Atribución-NoComercial 3.0 Unported.