2008-11-21T05:35:00.000-08:00

RECREATIONAL MORPHOMETRY

WATCHING SCIENTIFIC MEASUREMENTS WITH ELEMENTARY GEOMETRY .
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MOTIVATION

Wanted to choose only two numbers

from wich grew diversity in a

geometric-recreational look .

To attempt the most simple geometric look

we have choosen only a few values .

Actually be reduced to only three :

- values we call g and j

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

We explain the origen of ''g +j '' in an image

exposed near the bottom of this page

entitled '' STARTING NUMBERS '' .

The series 255 can be identified with

the following items :

breath , sigh , blow , run ...

To the left are some pictures

representing this concepts .

More , in this article : ''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 .

There is another series that is related

with the series 255 and that we use

frequently here , it's the serie ( 1+1/2+1/16+1/32 )

On the road , combining g and j

and the series (1+1/2+1/16+1/32) we performed

a pretty good approximation to ' Pi ' .

Related to that triangle whose legs

are g and j is one whose legs are

1 and 1/2( square root of two)

So that the hypothenuse has a value

of square root of (1+1/2) that we call d

And is this number d that we apply

frequently in our geometric games .

E.g. see the picture entitled

'' monday's shell algorithm '' .

**A brief look at : [Egg size,weight and fresh egg density of the scaled-sided merganser Mergus squamatus in south prymorye ,Rusia . Diana Solovievna & Valery Shokhin . Wildfowl (2008) 58 :106-111 .]

from the table 1 :

--egg length range measurements : 55.3 mm to 68.3 mm.

55.3 = 4Pi(1+1/2+1/16+1/32)^18

68.3 = 2Pi(1+1/2+1/16+1/32)^15

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** One value from this paper : [Composition of wood duck eggs in relation to egg size , laying sequence and skipped days of laying .Robert A. Kennamer et al. The Auk 114(3);479-487,1997] .
- egg length (mean value) : 50.05 mm

- 50.05 divided by (1+1/2+1/16+1/32) = 10 Pi (-0.012)
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** From : [Variation in the size and shape of Darwin's finch eggs . P. R. Grant . The Auk 99 : 15-23 . January 1982 ]

measurements of Zenaida galapagoensis :

-- clutch 1 , egg length (mean)= 27.66 mm :

(2Pi) x (1+1/2+1/16+1/32)^18

-- clutch 2 , egg length (mean)= 28.06 mm :

[4Pi /( g+j ) ]x(1+1/2+1/16+1/32)^18

-- species Geospiza difficilis , clutch 3

egg length (mean) = 17.56 mm :

(Pi/2)(1+1/2+1/16+1/32)^20

-- Geospiza difficilis , clutch 1 and clutch 4 . A case that applies the inverse of a parameter

egg length (mean) = 18.08 mm :

(2/Pi )(1+1/2+1/16+1/32)^22

-- Nesomimus parvulus , clutch 1

egg length (mean) = 26.45 mm :

12Pi(1+1/2+1/16+1/32)^19

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SOME GEOMETRIC OBSERVATIONS IN BIOLOGY .

Using values described in this page as '' Symmetry g + j '' , we've arranged two sets :

-> SET OF 15 ELEMENTS ( figure at right )

-> SET OF 22 ELEMENTS . According to an economy's principle ruling in Nature we suppose an overlapping in the origin , that is , inititial 8 elements .

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- The number of cells in the vulva of Caenorhabditis elegans worm are 22 . that is , 1+2+4+(8)+4+2+1

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- The number of all neurons are 302 = 22 +[(1+2+4)+(4+2+1)]20 . see figure at right .

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- MicroRNAs shows typically 21 or 22 nucleotids in length .

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-> A -DNA shows an average of 11 base pairs per turn of helix.

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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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-> The Myoglobin molecule of many species has 154 a.a. = 7(22)

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->Dissacharides 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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-> Cycles in solar activity influence on the biosphere. eg , sunspots are going throug cycles of

11 years .

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

RECREATIONAL GEOMETRY OF PHYSICAL CONSTANTS

2008-03-22T14:47:00.000-07:00

through the "magnifying glass" ()()()()()()()()()()()()()()()()()()()()()()()()()()()() Past year I bought a nice device .

without trade mark I call it monday ,

because the day I bought it .

Like a special lens it's able

to watch scientific numbers

under a geometrical point of view,

applying one set of few parameters

(see images in this page)

To test monday's skills

we'll gather all type of data .

Searching in the internet's published issues

(taking into account the significant figures only) .

At the bottom of this page

there is a collection of

'' geometric - entertainment '' in wich

we play with the significant figures

of some physical constants .

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

biology and geometry

RECREATIONAL GEOMETRY OF PHYSICAL CONSTANTS