The Golden Ratio. English

8/16/2019 The Golden Ratio. English

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The Measure of Beauty Created by GodTHE GOLDEN RATIO

What do the pyramids in Egypt, Leonardo da Vinci's portrait of the Mona Lisa,

sunowers, the snail, the pine cone and your ngers, all have in common?

he answer to this !uestion lies hidden in a series of num"ers discovered "y the

#talian mathematician, Leonardo $i"onacci% he characteristic of these num"ers,

&nown as the $i"onacci num"ers, is that each one is the sum of the preceding two

num"ers%

$i"onacci num"ers have an interesting feature% When you divide one num"er in the

series "y the num"er "efore it, you o"tain num"ers very close to one another%

#n fact, this num"er is ed after the ()th in the series and is &nown as the *+olden

atio%*

SPEAKER:

he eamples of the golden ratio that you will "e seeing in this lm, and that eist

in our own "odies and in all living things in nature, are -ust a few of the proofs that

+od has created all things with a measure% #n one verse .e reveals that/

God has ao!"ted a #easure for a$$ th!"%s& 'Surat at(Ta$a)* +,

THE H-MAN BOD. AND THE GOLDEN RATIO

When conducting their research or setting out their products, artists, scientists and

designers ta&e the human "ody, the proportions of which are set out according to

the golden ratio, as their measure%

Leonardo da Vinci and Le 0or"usier used this ratio in their designs%

he human "ody, proportioned according to the golden ratio, is also ta&en as the

"asis in the 1eufert, one of the most important reference "oo&s of modern2day

architects%

he *ideal* proportional relations that are suggested as eisting among variousparts of the average human "ody and that approimately meet the golden ratio

values can "e set out in a general plan%

he t3s ratio in the ta"le "elow is always e!uivalent to the golden ratio%

t3s 4 (%5(6

.owever, it may not always "e possi"le to use a ruler and nd this ratio all over

people7s faces, "ecause it applies to the 8ideali9ed human form: on which scientists

and artists agree%


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he rst eample of the golden ratio in the average human "ody is that when the

distance "etween the navel and the foot is ta&en as ( unit, the height of a human

"eing is e!uivalent to (%5(6%

;ome other golden proportions in the average human "ody are/

he distance "etween the nger tip and the el"ow 3 the distance "etween thewrist and the el"ow,

he distance "etween the shoulder line and the top of the head 3 the head

length,

he distance "etween the navel and the top of the head 3 the distance

"etween the shoulder line and the top of the head,

he distance "etween the navel and &nee 3 the distance "etween the &nee

and the end of the foot%

The Hu#a" Ha"d

SPEAKER

ur ngers have three sections% he proportion of the rst two sections to the full

length of the nger, gives the golden ratio% his does not, of course, apply to the

thum" with its two -oints%

=ou can also see that the proportion of the middle nger to the little nger is also a

golden ratio%

=ou have hands, and the ngers on them consist of ) sections% here are @ ngers

on each hand, and only 6 of these are articulated according to the golden num"er/

, ), @, and 6 t the $i"onacci num"ers%

The Go$de" Rat!o !" the Hu#a" /a0e

SPEAKER here are several golden ratios in the human face%

$or eample, the total width of the two front teeth in the upper -aw over their

height gives a golden ratio%

he width of the rst tooth from the centre to the second tooth also yields a golden

ratio%

SPEAKER

hese are the ideal proportions that a dentist may consider%

;ome other golden ratios in the human face are/


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he length of face 3 the width of face,

he distance "etween the lips and where the eye"rows meet 3 the length of

nose,

he length of face 3 the distance "etween tip of -aw and where the eye"rows

meet, he length of mouth 3 the width of nose,

he width of nose 3 the distance "etween nostrils,

he distance "etween pupils 3 the distance "etween eye"rows%

The Go$de" Rat!o !" the Lu"%s

#n a study carried out "etween (A6@ and (A6B, the Cmerican physicist, Druce West

and professor of medicine, Cry +old"erger, revealed the eistence of the golden

ratio in the structure of the lung%

>ne feature of the networ& of the "ronchi that constitutes the lung is that it is

asymmetric% $or eample, the windpipe divides into two main "ronchi, one long on

the leftF and the other short on the rightF% his asymmetrical division continues

into the su"se!uent su"divisions of the "ronchi% #t was determined that in all these

divisions the proportion of the short "ronchus to the long was always (3(%5(6%

Cll this information once again shows the superior nature of our Lord7s creation% #n

verses of the Gur7an it is revealed that +od created man 8within a proportion/:

He 1ho 0reated you a"d for#ed you a"d roort!o"ed you a"d asse#b$ed

you !" 2hate3er 2ay He 2!$$ed& 'Surat a$(I"4tar* 5(6,

THE GOLDEN RECTANGLE AND THE SPIRALS

C rectangle, the proportion of whose sides is e!ual to the golden ratio, is &nown as

a *golden rectangle%* Let us now eamine the features of this golden rectangle,

together/

C rectangle whose sides are ( and (%5(6 units long is a golden rectangle%Let us assume a s!uare drawn along the length of the short side of this rectangle

and draw a !uarter circle "etween two corners of the s!uare%

hen, let us draw a s!uare and a !uarter circle on the remaining side and do this

for all the remaining rectangles in the main rectangle%

When you do this you will end up with a spiral%

he Dritish aesthetician, William 0harlton, eplains the way that people nd the

spiral pleasing and have "een using it for thousands of years stating that we nd

spirals pleasing "ecause we can visually follow them with ease%


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he spirals "ased on the golden ratio contain the most incompara"le structures you

can nd in nature%

he rst eamples we can give of this, are the spiral se!uences on the sunower

and the pine cone% his is one of the many eamples of how Clmighty +od has

created all things awlessly and with a proportion%

The Stru0ture of Seashe$$s

When investigating the shells of mollus&s, the form and the structure of the internal

and eternal surfaces of the shells attracted the scientists' attention/

The internal surface is smooth, the outside one is uted. The mollusk body is inside

shell and the internal surface of shells should be smooth. The outside edges of the

shell augment a rigidity of shells and, thus, increase its strength. The shell forms

astonish by their perfection and protability of means spent on its creation. The

spiral's idea in shells is expressed in the perfect geometrical form, in surprising

beautiful, "sharpened" design.

he shells of most mollus&s grow in a logarithmic spiral manner%

here can "e no dou"t, of course, that these animals are unaware of even the

simplest mathematical calculation, let alone logarithmic spirals%

;o how is it that the creatures in !uestion can &now that this is the "est way for

them to grow?

.ow do these animals, that some scientists descri"e as *primitive,* &now that this

is the ideal form for them?

#t is impossi"le for growth of this &ind to ta&e place in the a"sence of a

consciousness or intellect%

hat consciousness eists neither in mollus&s nor, despite what some scientists

would claim, in nature itself%

#t is totally irrational to see& to account for such a thing in terms of chance%

his structure can only "e the product of a superior intellect and &nowledge%

Clmighty +od has created these living things to "e awless%

#n one verse of the Gur7an it is revealed how +od reigns over all things with .issuperior &nowledge, and how human "eings must reect on our Lord7s matchless

creative artistry/

My Lord e"0o#asses a$$ th!"%s !" H!s 7"o2$ed%e so 2!$$ you "ot ay

heed8 'Surat a$(A"9a#* 6,

+rowth of this &ind was descri"ed as *gnomic* "y the "iologist ;ir H'Crcy

hompson, an epert on the su"-ect, who stated that it was impossi"le to imagine a

simpler system, during the growth of a seashell, than which was "ased on widening

and etension in line with identical and unchanging proportions% Cs he pointed out,the shell constantly grows, "ut its shape remains the same%


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>ne can see one of the "est eamples of this type of growth in a nautilus, which is

-ust a few centimeters in diameter%

0ros"ie Morrison descri"es this growth process, which is eceptionally diIcult to

plan even with human intelligence, stating that along the nautilus shell, an internal

spiral etends, consisting of a num"er of cham"ers with mother2of2pearl lined walls%

Cs the animal grows, it "uilds another cham"er at the spiral shell mouth larger thanthe one "efore it, and moves forward into this larger area "y closing the door

"ehind it with a layer of mother2of2pearl%

he scientic names of some other marine creatures with logarithmic spirals

containing the diJerent growth ratios in their shells are/ Haliotis Parus, !olium

Perdix, urex, #calari Pretiosa%

The Go$de" Rat!o !" the Hear!"% a"d Ba$a"0e Or%a"

he cochlea in the human inner ear serves to transmit sound vi"rations%

his "ony structure, lled with uid, has a logarithmic spiral shape with a ed

angle of B)K) containing the golden ratio%

Hor"s a"d Teeth That Gro2 !" a S!ra$ /or#

Eamples of curves "ased on the logarithmic spiral can "e seen in the tus&s of

elephants and the now2etinct mammoth, lions' claws and parrots' "ea&s%

he eperia spider always weaves its we"s in a logarithmic spiral%

Cmong the micro2organisms &nown as plan&ton, the "odies of glo"igerinae,

planor"is, vorte, tere"ra, turitellae and trochida, are all constructed on spirals%

Cmmonites, which are today etinct and found only in fossil form, also have shells

that grow logarithmically% 1either is the spiral form in the animal &ingdom limited to

mollus& shells alone% he horns of such animals as the antelope, the mountain goat

and the ram also grow in spirals "ased on the golden proportion%

The Go$de" Rat!o !" DNA

he H1C molecule in which all the physical features of living things are stored, has

also "een created in a form "ased on the golden ratio%

H1C consists of two intertwined perpendicular helies%

he length of the curve in each of these helies is ) angstroms and the width (

angstroms% ( angstrom is one hundred millionth of a centimeter%F

( and ) are two consecutive $i"onacci num"ers%

Cll this information is -ust some of the important proof that the universe wascreated "y a su"lime intelligence, in other words, that +od created the universe

and all things in it from nothing%


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#n the Gur7an, +od has called upon "elievers to reect on this evidence%

Cnyone who considers the eamples around him in the light of his conscience will

see this manifest truth% he perfection of our Lord7s creative artistry has "een

revealed in these terms in the Gur7an/

; .ou 2!$$ "ot 4"d a"y


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.ad we "egun counting in the opposite direction, then we would have o"tained the

same num"er of leaves, "ut at a diJerent num"er of revolutions% he num"er of

turns in each direction and the num"er of leaves encountered during these, reveal

three consecutive $i"onacci num"ers%

hese se!uential forms may "e circular or spiral, depending on the species of plant%

>ne of the most important results of this special se!uencing is that leaves are

arranged so as not to cast shadows over one another%

Cccording to these proportions, &nown as 8leaf divergence: in "otany, the order in

the way leaves are arranged around the stem has "een determined with particular

num"ers%

his arrangement is "ased on an eceedingly comple calculation%

#f 1 is the num"er of revolutions we need to ma&e, "eginning at one leaf, until we

encounter another leaf at the same level, and if N is the num"er of leaves

encountered during this cycle, then N31 fraction is the 8leaf divergence: that eists

in plants%

Leaf divergence 4 1um"er of leaves in a leaf cycle3num"er of revolutions

$ractions peculiar to some plants are as follows/

2 (3 in meadow plants grassesF

2 (3) in marsh plants

2 3@ in fruit trees apple trees, for eampleF

2 )36 in "anana species,

2 @3() in "ul"ous plants%

SPEAKER

THE 1A. THAT EER. TREE /ROM THE SAME SPECIES IS A1ARE O/ THIS

RATIO AND ABIDES B. THE PROPORTION DETERMINED /OR IT IS A GREAT

MIRACLE&

.ow does a "anana tree, for eample, &now a"out this fraction and how, no matter

where it may "e in the world, is it a"le to a"ide "y it?

Cccording to this calculation, when you "egin from any leaf and ma&e 6 revolutions

around any "anana tree trun&, you will encounter another leaf at the same level

and at the same time encounter ) leaves in this cycle%

1o matter where you go in the world, from ;outh Cfrica to Latin Cmerica, this

fraction never changes%


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mniscient +od Who encodes such a proportion in the genetic

structure of living things and creates them with that information%

he numerical miracles we encounter in plants go further than these%

Clthough the "ranches we see on the trees around us may appear to "e arranged

hapha9ardly at rst glance, they, too, are actually arranged according to an

eceptionally comple plan and mathematical calculation%

SPEAKER

Dotanists have identied the golden ratio num"ers inherent in the "ranching of a

growing plant%We may now consider the eample of the snee9ewort plant% Let us now loo& at the

relationship "etween "ranching and the golden proportion in this plant%

Cs the plant grows, a new "ranch emerges from every "ud, and a new "ranch from

that one%

#f the num"er of "ranches in a hori9ontal plane is counted, then $i"onacci num"ers

can "e seen%

he $i"onacci series is an important &ey to understanding the ne calculation and

arrangement in plants%

his shows the order and aesthetics in leaves and owers arranged according to

the $i"onacci series%

he fact that plants are shaped according to specic mathematical formulae, is one

of the most evident proofs that they have "een specially created%

he sensitive measures and "alance in plant atoms and H1C also eist in the

plant7s eternal appearance%

>ther proofs of creation involving the golden ratio include some owers, seeds and

fruits%

he sunower is one of the nest eamples on this su"-ect%

#f you pic& up and eamine a sunower, you will see that its seeds are arranged in

spirals%

Cnd if you start to count all the seeds in the spirals turning to right and left, you will

nd two consecutive num"ers from the $i"onacci series%

his is certainly not limited to the sunower alone%

he leaves of densely seeded plants, such as the ca""age, also form spirals runningto right or left around a central point, as in the sunower%


9/26

Haisies and pine cone scales are also set out in right and left spirals%

#f you count these one "y one, you will again o"tain num"ers "ased on the

$i"onacci series, in other words, on the golden ratio%

hese num"ers in the spirals in plants will "e/

@36 and 63() in pine cones,

63() in pineapples,

(3) in the central orets of the daisy,

Cnd (3), )3@@ and @@36A in sunowers%

Evidence of +od7s awless creation can "e found in all this ne measure and

regularity% he awless creation of plants has "een revealed in a verse from the

Gur7an, and we are told that this is also important proof for "elievers/

It !s He 1ho se"ds do2" 2ater fro# the s7y fro# 2h!0h 1e br!"% forth

%ro2th of e3ery 7!"d* a"d fro# that 1e br!"% forth the %ree" shoots a"d

fro# the# 1e br!"% forth 0$ose(a07ed seeds* a"d fro# the sathes of the

date a$# date 0$usters ha"%!"% do2"* a"d %arde"s of %raes a"d o$!3es

a"d o#e%ra"ates* both s!#!$ar a"d d!ss!#!$ar& Loo7 at the!r fru!ts as they

bear fru!t a"d r!e"& There are s!%"s !" that for eo$e 2ho be$!e3e& 'Surat

a$(A"a#* ,

THE GOLDEN RATIO IN THE MICRO1ORLD

+eometrical shapes are "y no means limited to triangles, s!uares, pentagons or

heagons%

hese shapes can also come together in various ways and produce new three2

dimensional geometrical ones%

he cu"e and the pyramid are the rst eamples that can "e cited% #n addition to

these, however, there are also such three2dimensional shapes as the tetrahedron,

octahedron, dodecahedron, icosahedron and heahedron, that we may never

encounter in our daily lives and whose names we may never even have heard of%

he dodecahedron consists of ( pentagonal faces, and the icosahedron of Otriangular ones%

;cientists have discovered that these shapes can all mathematically turn into one

another, and that this transformation ta&es place with ratios lin&ed to the golden

ratio%

hree2dimensional forms that contain the golden ratio are very widespread in

microorganisms%

Many viruses have an icosahedron shape% he "est &nown of these is the Cdeno

virus%


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he protein sheath of the Cdeno virus consists of @ protein su"units, all regularly

set out%

he ( su"units in the corners of the icosahedron are in the shape of pentagonal

prisms% od2li&e structures protrude from these corners%

he rst people to discover that viruses came in shapes containing the golden ratiowere Caron Plug and Honald 0aspar, from Dir&"ec& 0ollege in London, in the (A@Os%

he rst virus they esta"lished this in was the polio virus% he hino ( virus has

the same shape as the polio virus%

Why is it that viruses have shapes "ased on the golden ratio, shapes that are hard

for us even to visuali9e?

Caron Plug, who discovered these shapes, eplains/

$y colleague !onald %aspar and & shoed that the design of these iruses could

be explained in terms of a generali(ation of icosahedral symmetry that allosidentical units to be related to each other in a )uasi*e)uialent ay ith a small

measure of internal exibility. +e enumerated all the possible designs, hich hae

similarities to the geodesic domes designed by the architect . -uckminster uller.

Hoeer, hereas uller's domes hae to be assembled folloing a fairly elaborate

code, the design of the irus shell allos it to build itself./

Plug's description once again reveals a manifest truth%

here is a sensitive planning and a perfect structure even in viruses, regarded "y

scientists as *one of the simplest and smallest living things%*

his structure is a great deal more successful than and superior to those of

Duc&minster $uller, one of the world's most eminent architects%

SPEAKER

he dodecahedron and icosahedron also appear in the silica s&eletons of

radiolarians, single2celled marine organisms%

;tructures "ased on these two geometric shapes, li&e the regular dodecahedron

with feet2li&e structures protruding from each corner and the various formations ontheir surfaces, ma&e up the varying "eautiful "odies of the radiolarians%

The Go$de" Rat!o !" S"o2


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The Go$de" Rat!o !" Phys!0s

SPEAKER

=ou encounter $i"onacci series and the golden ratio in elds that fall under the

sphere of physics%

When a light is held over two contiguous layers of glass, one part of that light

passes through, one part is a"sor"ed, and the rest is reected% What happens is a

*multiple reection%* he num"er of paths ta&en "y the ray inside the glass, "efore

it emerges again, depends on the num"er of reections it is su"-ected to% #n

conclusion, when we determine the num"er of rays that re2emerge, we nd that

they are compati"le with the $i"onacci num"ers%

The Go$de" Rat!o Is Gods Creat!o"SPEAKER

he fact that a great many unconnected animate or inanimate structures in nature

are shaped according to a specic mathematical formula, is one of the clearest

proofs that these have "een specially created%

he golden ratio is an aesthetic rule well &nown and applied "y artists%

Wor&s of art "ased on that ratio represent aesthetic perfection%

Nlants, galaies, microorganisms, crystals and living things created according to

this rule imitated "y artists are all eamples of +od's superior artistry%

+od reveals in the Gur'an that .e has created all things with a measure%

;ome of these verses read/

; God has ao!"ted a #easure for a$$ th!"%s& 'Surat at(Ta$a)* +,

; E3eryth!"% has !ts #easure 2!th H!#& 'Surat ar(Ra9d* 6,


12/26

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13/26

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14/26

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15/26

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18/26

he internal surface is smooth, the outside one is uted% he mollus& "ody is inside

shell and the internal surface of shells should "e smooth% he outside edges of the

shell augment a rigidity of shells and, thus, increase its strength% he shell forms

astonish "y their perfection and prota"ility of means spent on its creation% he

spiral's idea in shells is epressed in the perfect geometrical form, in surprising

"eautiful, *sharpened* design% www%goldenmuseum%comF

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19/26

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20/26


21/26

(3 in meadow plants grassesF,

Data&lQ& "it&ilerinde (3),

(3) in marsh plants,

Meyve aRaUlarQnda elmaF 3@,

3@ in fruit trees apple treesF,

Mu9 tSrlerinde )36,

)36 in "anana species,

;oRangillerde @3()

@3() in "ul"ous plants%

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80aspar ile "en, &Sresel "ir virSs &QlQfQ iUin optimum en uygunF tasarQmQn

i&osahedron tar9Q "ir simetriye dayandQRQnQ gYsterdi&% DYyle "ir dS9enleme

"aRlantQlarda&i sayQyQ en a9a indirir% MimarF Duc&minster $uller7in yarQ &Sresel

-eode9i& &u""elerinden UoRu da "en9er "ir geometriye gYre inXa edilir% Du&u""elerin oldu&Ua ayrQntQlQ "ir Xemaya uyulara& monte edilmeleri gere&ir% .al"u&i

"ir virSs &QlQfQ, alt "irimlerinin esne&liRinden YtSrS &endi &endini inXa eder%: 32. 8lug

$olecules on 9rand #cale/, :e #cientist, ;=, ;?@A7

8My colleague Honald 0aspar and # showed that the design of these viruses could

"e eplained in terms of a generali9ation of icosahedral symmetry that allows

identical units to "e related to each other in a !uasi2e!uivalent way with a small

measure of internal ei"ility% We enumerated all the possi"le designs, which have

similarities to the geodesic domes designed "y the architect % Duc&minster $uller%

.owever, whereas $uller's domes have to "e assem"led following a fairly ela"orate


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+od has appointed a measure for all things% ;urat at2ala!, )F

Everything has its measure with .im% ;urat ar2a'd, 6F

Delgesel sQrasQnda arada, ve "elgesel sonunda/

his lm is "ased on the wor&s of .arun =C.=C%$or more information, please visit www%harunyahya%com
http://www.harunyahya.com/http://www.harunyahya.com/

The Golden Ratio. English

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