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Forums > Social Chat > The divine proportion - The Da Vinci Code

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DeepSoulSheep
GOLD Member since Sep 2002

DeepSoulSheep

Carpal \'Tunnel
Location: Berlin, Ireland

Total posts: 2617
Posted:So my friends reading this book and I'm thinking I'd like to read it when he's done. It has introduced this idea of the divine proportion which I find astonishing.

I've copied and pasted the below from another board, cause I've neither read the book nor have I the inclination to re-type and make mistakes...

Quote:
The author, Dan Brown, has done an incredible job of fashioning a work of fiction based on fact. It's difficult occasionally to tell the dividing line between the two, and that sent me surfing the Internet for information. The page before the Prologue states that "All descriptions of artwork, architechture, documents, and secret rituals in this novel are accurate." It also confirms that the Priory of Sion, a secret society founded in 1099 is a real organization, and that Opus Dei, is truly a Catholic sect with headquarters in New York City.

One of the first subjects Brown introduces in discussing the works of Da Vinci is the number PHI. (Clues in Da Vinci's work lead the way to resolving Sauniere's death, so Brown presents facts about the work to move the story forward)

As a musician, I never had the chance to take classes in other forms of art, so I've never been introduced to the concept of PHI in art class. The number 1.618 is PHI. It's also known as the "Divine Proportion." Brown writes "PHI is generally considered the most beautiful number in the universe."

PHI is derived from the Fibonacci sequence (more on this later). It turns out that PHI has a role as a natural building block of nature. Plants, animals, and even humans possess dimensional properties which adhere to the ratio of PHI to 1.

For example, in a honeybee community, the females outnumber the males by 1.618 to 1.

The ratio of each spiral to the next on a chambered Nautilus' shell is 1.618 to 1.

"Sunflower seeds grow in opposing spirals." The ratio of each spiral to the next is PHI to 1. This is also true of spiraled pinecone petals, leaf arrangement on plant stalks and insect segmentation.

Da Vinci studied corpses and discovered the Divine Proportion in human bone structure. The distance from the tip of your head to the floor, compared to the distance from your navel to the floor is PHI to 1.

The distance from your shoulder to your finger tips, divided by the distance from your elbow to your fingertips will give you PHI. You'll find the same ratio with hip to floor divided by knee to floor, finger joints, toes, and spinal divisions.

Brown presents all this information in a classroom setting, and it's infinitely more interesting than my dry recitation of facts. I responded the same way as the fictional class, enjoying each example he provided.

The point of this, is that we find that it's not limited to nature, but it's been used by artists and architects. The Parthenon, the pyramids in Egypt and the United Nations Building all use the Divine Proportion. Da Vinci, Michaelangelo, Durer and many other artists used the proportion in their paintings, and Beethoven, Mozart, Bartok, Shubert and Debussy are just a few musicians who have also used it in their compositions.

Fascinating, isn't it? Get the book, and see how Dan Brown carries it through his story.





So I just measured and divided the distance from my shoulder to the tip of my finger by the distance from my elbow to the tip of my hand and got 1.6 aaghghhghh. ubbloco

Has anyone read this or hear of it before.....pretty interesting at least.... smile



I live in a world of infinite possibilities.

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Dunc
GOLD Member since Aug 2003

Dunc

playing the days away
Location: The Middle lands, United Kingd...

Total posts: 7263
Posted:Nope never heard of it but sounds pretty interesting.....I'll have some reading to do later on now!!

Cheers DSS beerchug


Let's relight this forum ubblove

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originalsmit
SILVER Member since Aug 2003

originalsmit

addict
Location: nottingham, england. cornwall ...

Total posts: 469
Posted:well i have heard of the fibbonaci sequence 1+1=2 then 1+2=3 then 3+2=5 etcetc
but PHI is a new one to me i guess its a number that can be defined to an infinite degree. like PI good old 3.14952 the radius of a circle.
beeing a former bee keeper i find it quite odd the statistic about male to female bees as drones(males) are produced only during the swarming season ie the summer months.
as soon as it gets cold the males are all killed off as they are useless to have hanging round the hive using valuable honey.
so the population is always in gradual increase or sharp decline steady for a very short time.
still makes you think


my original signature was tooo long.
this one is shorter

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Narr


Narr

(*) (*) .. for the gnor ;)
Location: sitting on the step

Total posts: 2568
Posted:yeah, i watched something that touched on this on BBCprime a few weeks ago.. was really interesting.
theres a guy in the states that has made a mask, blueprint type thing of just lines and angles to fit the human face. everything follows this rule, and he found that it only fits people that are considered to be beautiful or handsome. he showed some examples and it was absolutely facsinating to see...


she who sees from up high smiles

Patrick badger king: *they better hope there's never a jihad on stupidity*

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Doc Lightning
GOLD Member since May 2001

Doc Lightning

HOP Mad Doctor
Location: San Francisco, CA, USA

Total posts: 13920
Posted:I haven't read it yet. But when I was on my surgery rotation, I remember that one morning as we rounded, we noticed that six of our patients had the book in their rooms.

I need to read it at some point. Thanks for reminding me.


-Mike )'(
Certified Mad Doctor and HoP High Priest of Nutella

"A buckuht 'n a hooze!" -Valura

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay, United Kin...

Total posts: 7330
Posted:was introduced to me as the 'golden ratio'.



you can approximate it by using continued a fraction: 1+1/(1+1/1+1...)



of course phi is an irrational number so we can never express it exactly as a fraction but this is a nice way of getting an approximation.



i want a house where all the rooms are constructed with width:length ratio as 1:phi.

ceiling heights will just be specified as 'higher than you think will ever be necessary'.




Non-Https Image Link




this page is quite a nice introduction.



"maths just is."


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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polythene


veteran
Location: London/ Surrey

Total posts: 1359
Posted:If you like this kind of thing, another good one is 'patterns in nature' I think by Phillip Ball. Lots on spiral structures, bubbles and things, info about the martian 'fossils' that had a brief stint in the newspapers. Anyone with inclinations to science and art (like me!) will love it smile

The optimist claims that we are living in the best of all possible worlds.
The pessimist fears this is true.

Always make time to play in the snow.

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spritie
SILVER Member since Sep 2001

spritie

Pooh-Bah
Location: Galveston, TX, USA

Total posts: 2014
Posted:Yup, the golden ratio is what it was called in one of my many math classes in college. It oddly enough popped up in several of my non-math classes that year as well.

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Dom
BRONZE Member since Dec 2001

Dom

Carpal \'Tunnel
Location: Bristol, UK

Total posts: 3009
Posted:Yep, hear of it. The Golden Ratio that makes nature beautiful.

Although my house would be based on natures shapes that are formed using the golden ratio (could god please reincarnate Gaudi) and uneven floors and ceilings (add Hundertwasser to the list).

"Straight lines are utterly alien to human beings, to life, and to the whole of creation" - Hundertwasser


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simian


simian

110% MONKEY EVERY TIME ALL THE TIME JUST CANT STOP THE MONKEY
Location: London

Total posts: 3149
Posted:nah man, straight lines rule wink ubblol

"Switching between different kinds of chuu chuu sometimes gives this "urgh wtf?" effect because it's giving people the phi phenomenon."

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay, United Kin...

Total posts: 7330
Posted:Quote:
could god please reincarnate Gaudi



ditto.

who's god this week?


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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bubblishis


False Eyelash
Location: New York City

Total posts: 346
Posted:I wont volunteer to be God this week. But I did read the DaVinci Code. It's all the rage right now.

And I'll say it's excellent. Quite a page turner. Very intriguing. Mary Magdalene as the holy grail - what could be more perfect? He should have included a bibliography though - it was really hard to find the line between fact and fiction. Not to mention it'd be nice to have a resource for more info.



All the freaky people make the beauty of the world.

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Necrus


Necrus

member
Location: Greece/Athens

Total posts: 113
Posted:I don't want to be rude,but maybe mr.Dan Brown and everyone who cared about symmetry in nature or anything like it should study ancient Greek philosophers,architects.mathematicians etc.

The first one to speak about to mention and use Φ in art,a greek letter pronounced PHI like written above,is Pheidias I think,a great ancient greek architect&sculpturer.He found about Φ,also known as the number of divine proportion/symmetry)at least 1000-1500 earlier than Da Vinci. . .

Da Vinci was a man with a brilliant mind ubbidea(he was professioned with almost anything concerning science and nature at his time) but no one can deny he studied ancient Greek philosophers like Aristotle,Archimides,Pythagoras,Thales etc. . .


Metal Rulezzzzzz!!!!!!!!!!!

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Singed Piper (formerly Mark1)


Singed Piper (formerly Mark1)

resident bagpiper
Location: Vermont, USA

Total posts: 342
Posted:just a note about pi,
it is
3.141592... unlike what was stated above
also the first 20 digits have a nifty poem/mnemonic to remember them by

sir, i send a rhyme excelling
in sacred truth and rigid spelling
numerical sprites elucidate
for me the lexicon's dull weight

read the comma as a decimal point, and count the number of letters in each word
i.e. 3 . 1 4 1 5 9 2 ....

anyway, slainte mhath beerchug


Q:What's the difference between the Great Highland Bagpipes and the Northumbrian Pipes?
A:The Great Highland Pipes burn longer.

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polythene


veteran
Location: London/ Surrey

Total posts: 1359
Posted:The number talked about above is phi, not pi.

The optimist claims that we are living in the best of all possible worlds.
The pessimist fears this is true.

Always make time to play in the snow.

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay, United Kin...

Total posts: 7330
Posted:original smit said:
Quote:
like PI good old 3.14952 the radius of a circle.



it is kinda wrong.
the number and the definition actually.

the number is as above and is defined as "the ratio of the circumference to the diameter of a circle".

there are lots of cunning ways of working out pi to lots of decimal places (well, cunning in the maths sense of the word smile).

working out phi is a bit trickier...
read this if you really wanna know.


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay, United Kin...

Total posts: 7330
Posted:Quote:
I don't want to be rude,but maybe mr.Dan Brown and everyone who cared about symmetry in nature or anything like it should study ancient Greek philosophers,architects.mathematicians etc.



easy necrus smile

i'm certain that dan brown will have studied the ancient greek mathematicians work extensively.

history of phi with reference to euclid's elements:

Code:In Book 6, Proposition 30, Euclid shows how to divide a
line in mean and extreme ratio which we would call "finding the
golden section G point on the line".

<-------- 1 --------->
A G B
----------------------
g 1g

Euclid used this phrase to mean the ratio of the smaller part of
this line, GB to the larger part AG (ie the ratio GB/AG) is the
SAME as the ratio of the larger part, AG, to the whole line AB (ie
is the same as the ratio AG/AB). If we let the line AB have unit
length and AG have length g (so that GB is then just 1g) then
the definition means that:

GB/AG = AG/AB i.e. using the lengths of the sections (1-g)/g = g/1

which we rearrange to get 1 g = g^2

Notice that earlier we defined Phi2 as Phi+1 and here we have g^2 = 1g or g^2+g = 1.
We can solve this in the same way as for Phi and we find that:

g=(-1+sqrt(5))/2 or g=(-1-sqrt(5))/2

So there are two numbers which when added to their squares
give 1. For our geometrical problem, g is a positive number so
the first value is the one we want. This is our friend phi also
equal to Phi1 (and the other value is merely Phi).


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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Necrus


Necrus

member
Location: Greece/Athens

Total posts: 113
Posted:If you really wanna understand maths,science or even nature learn Greek.Not today's Greek but ancient Greek...

Check this out

I suggest to search this site thoroughly...I'm sure you'll find something interesting and moreover something new....

If someone does,I'd like to hear his opinion...


Metal Rulezzzzzz!!!!!!!!!!!

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oli
SILVER Member since Jul 2003

not with cactus
Location: bristol/ southern eastern devo...

Total posts: 2052
Posted:yea ive heard phi,

its one of the solutions to x = 1 + 1/x which you can arrive at by defining it as the fraction 1+1/(1+1/(1+1/(1+1/(1+...) ))) as colman said. the fraction is fractal and is still the same when you take away the font part of it, and i think thats why you can do this.
the solution is (1+5^1/2)/2.

apparntly it occours pretty much anywhere in geometry where the number 5 is involved.

tis cool stuff tongue


Me train running low on soul coal
They push+pull tactics are driving me loco
They shouldn't do that no no no

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coleman
SILVER Member since Aug 2002

coleman

big and good and broken
Location: lunn dunn, yoo kay, United Kin...

Total posts: 7330
Posted:umm




Non-Https Image Link




this only gives pi to 2 decimal places.



pi, being an irrational number, cannot be expressed as a fraction at all so that method was only ever going to give an approximation.



i'm a bit on the fence about all this language code stuff.

i'm pretty sure that most of the bible codes are not what people make them out to be - some guy did the same skip code tests on moby dick and got similar results.

i believe the bible codes were statistically disproved using a very cleverly designed 'prediction of birth and death dates from the names of some rabbis' test.



thoth tarot uses coded hellenic language too.



as much as i want to believe, i think i'm slowly coming round to the opinion that if you look hard enough, you can find connections in everything.


"i see you at 'dis cafe.
i come to 'dis cafe quite a lot myself.
they do porridge."
- tim westwood

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Tao Star


Tao Star

Pooh-Bah
Location: Bristol

Total posts: 1662
Posted:Quote:
sir, i send a rhyme excelling
in sacred truth and rigid spelling
numerical sprites elucidate
for me the lexicon's dull weight

read the comma as a decimal point, and count the number of letters in each word
i.e. 3 . 1 4 1 5 9 2 ....



sonds harder to remember than pi to me!


I had a dream that my friend had a
strong-bad pop up book,
it was the book of my dreams.

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Bubbles_
SILVER Member since Nov 2004

Bubbles_

Carpal \'Tunnel
Location: mancunian, United Kingdom

Total posts: 3383
Posted:ok im currently reading the da vinci code now after been told by numerous people that i should read it.

this book is..... undescribable(sp?)!

im posting this to see what you all think too, not just the phi and 'divine proportion' but all the other bits Brown talks about in this book
i would like to say more on it but i want to finish it first. it has opened my eyes a lot and i find it fasinating! i wish i could discuss at length this book as well but i actually feel really small when i read it, there is just so much to comprehend and i think it may take me a few years to understand it fully (as in the historys and facts it includes, as well as the artistic side which i am wanting to learn more about).

i highly recomend it as a read, and i understand there is a film now in progress to be released next year. which i hope is identical to the book (as hollywood films have changed books before when making them into a film) because otherwise it would lose all of its meaning.

whether everything ive read in it so far is true or not i hope to discover, but ill be back once ive finished it (which wont be long because i cannot put it down!)

has anyone read it? or currently reading it? whats your view? ive been told to take it with a pinch of salt, but i think i almost want to believe it all true in a sense...

ok i have a kinda head freeze here so ill stop typing tongue


Disclaimer:im not responsible for what i say or do whether it be before,during and after drinking alcoholic substances (owned by BMVC).
Creater of Jenisms(TM)
Virginity like bubble,one prick all gone.

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MiG
GOLD Member since Apr 2004

MiG

Self-Flagellation Expert
Location: Bogged at CG, Australia

Total posts: 3415
Posted:I don't think too much of it IS true, but the great thing is that so much COULD be true...

Angels and demons is really quite good, too.


"beg beg grovel beg grovel"
"master"
--FSA

"There was an arse there, i couldn't help myself"
--Rougie

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Larry
SILVER Member since Oct 2005

Larry

Electro Ponce!
Location: Hull!, United Kingdom

Total posts: 383
Posted:well, i thought it was just us maths students who went on about things like this. someone give me a piece of paper and a pen and i'll show you what it's all about. (you know youre bored when u grafitti an accurate fibonacci spiral on your work!)

What're you looking at?
I assume you're being rhetorical?
What're you callin' me!?

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pricklyleaf
SILVER Member since Mar 2005

pricklyleaf

with added berries
Location: Manchester, England (UK)

Total posts: 1365
Posted:yeh, learnt a lot about golden proportion in art, and science at school. Read the Da vinci code a while back, the thing that annoyed me the most was not the whole fact\fiction stuff, I thought that was well done and thought provoking, but the last code to break, was so blatently obvious from the start what it was, yet they spent pages and pages trying to solv the easiest puzzle in the book. I practically shouting at the pages! Other than that I think it is a really good book, and definately worth the read.

Live like there is no tomorrow,
dance like nobody is watching
and hula hoop like wiggling will save the world.

What lies behind us and what lies before us are tiny matters compared to what lies within us.

Ralph Waldo Emerson

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FoxInDocs
SILVER Member since Jul 2005

FoxInDocs

Pooh-Bah
Location: Adelaide, SA, Australia

Total posts: 1848
Posted:interesting theories and/or facts? yes.
good book? ...i've read better. much better actually.


"i am exotic, and must keep my arms down" - Rougie

"i don't understand what penises have to do with getting married" - Foxie

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Domino
SILVER Member since May 2004

UnNatural Scientist - Currently working on a Breville-legged monkey
Location: Bath Uni or Shrewsbury, UK

Total posts: 757
Posted:Depends on how you define beautiful...

e^ ( i x PI ) = 1

That's a number that can't be written down to the power of a number that dosen't exist in the real world (i = sqaure root of minus one) times a number that can't be written down = 1

e = 2.717something and also pops up all over nature


Give me a lever long enough and a place to stand and I can beat the world into submission.

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NOn


activist for HoPper liberation.
Location: ffidrac

Total posts: 1643
Posted:well i haven't read the book, maybe i will... but i did once do a project about the golden section/ proportion/ ratio etc, history of, fibonacci, relationship to nature, use in architecture, design and all that. i can confirm, that lovely theory though it is, it drives you nuts after awhile, and i eventually came to the conclusion that you can find it ANYWHERE if you know where and how to look, which kind of takes the fun out of it somewhat. with a careful manipulation of maths, you could probably find any number...

there's one other measurement somewhere around the 2.2 mark that was named the modulor by le corbusier and used in his architecture... this also has some thing to do with the body... so equally divine i presume...

but, frequent though it is occurring in nature, there is a lot more to beauty in nature than just a number, you could make any object you wanted in this ratio, doesn't necessarily make it beautiful though

*divine proportion sceptic*


Aurinko freedom agreement reached 10th Sept 2006

if it makes no sense that's because it's NOn-sense.

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Larry
SILVER Member since Oct 2005

Larry

Electro Ponce!
Location: Hull!, United Kingdom

Total posts: 383
Posted:Written by: Domino

Depends on how you define beautiful...

e^ ( i x PI ) = 1

That's a number that can't be written down to the power of a number that dosen't exist in the real world (i = sqaure root of minus one) times a number that can't be written down = 1

e = 2.717something and also pops up all over nature



ha, bring on imaginary numbers, and exponentials!
wait til someone starts on 6 circles surrounding a circle of the same size! there's some wierd ideas on that!


What're you looking at?
I assume you're being rhetorical?
What're you callin' me!?

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TinklePants
GOLD Member since Jul 2005

TinklePants

Clique Infiltrator, Cunning Linguist and Master Debator
Location: Edinburgh burgh burrrrrr, Unit...

Total posts: 4217
Posted:i read the da vinci code earlier this yeah - a very exciting read. i decided to read browns brown's previous book, i think it was angels n demons, but it was exactly the same beginning and i gave up lol

Always use "so's your face" and "only on Tuesdays" in as many conversations possible

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Drudwyn


Drudwyn

Forget puppy power, Scrappy's just gay
Location: Southampton Uni

Total posts: 632
Posted:I hate Dan Brown. He may have some interesting ideas, and he's certainy a very good researcher, in that so many of the things that crop up in his books are taken from other sources or true. However I find it impossible to read his books, as the writing is so bad!

On another note, we, as humans are desgined to spot patterns, so give anyone a sequence of letters, or colours or a number, and they will spot it everywhere! However, Phi ratios do look beautiful, so there may be some truth to it...


Spin, bounce, be one with the world, because it is yours to enjoy...

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