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Fibonacci Sequence and the Golden Number

wagger

By wagger

108 comments


Have you ever wondered why four-leafed clovers are so rare? It’s because 4 isn’t a Fibonacci Number.

I’d never heard of these until I came across them in a book and googled it for more information. It’s absolutely fascinating (or mind-blowingly boring depending on your point of view)

This system was first discovered and understood by Leonardo Fibonacci in the 13th century and runs 0 1 1 2 3 5 8 13 21 34 55 89 144 etc.

Now we start counting flower petals – lily 3 Buttercup,wild rose, vinca 5 delphinium, coreopsis 8 marigold, cineraria 13 aster, chicory, black-eyed susan 21 plantain, pyrethrum 34 daisy, aster family 34,55,89. There are of course exceptions but when the numbers are averaged it will usually be a Fibonacci number.

The next appearance of the Fibonacci series is in spirals – sunflower centres, pine cones, pineapples etc If you look at a sunflower head you will see the florets or seeds are arrranged in two intersecting groups of spirals, one clockwise and one anticlockwise. The number of spirals will be 34 and 55, 55 and 89 or 89 and 144. Pineapples have eight rows of scales sloping left and 13 sloping right.

Of course, not all plants follow this system – some of the remainder – but not all – follow the Lucas numbers system – 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 etc. but the ratio of two successive numbers in each system is 1.6180339 or the greek phi.

I think we’ll leave phi – the golden number for another day as my brain hurts now.

More blog posts by wagger

Previous post: I've still got wet feet!

Next post: Fibonacci Sequence - here we go again!



Comments

 

Wow what a stunner great picture. The number 4 is not liked by numerologists, it also derives at times form 13 which is lucky for some but not for others. as 1+3=4

24 Nov, 2009

 

yet dna the basis of nearly all life is based on 4 nitrogenous bases. if not dna then rna also 4 nitrogenous bases. though the genetic code is in triplets. isnt science magic?

24 Nov, 2009

 

B****y confusing if you ask me!

24 Nov, 2009

 

well yes it's that too but so clever in a 'i dont understand it'

24 Nov, 2009

 

LOL

24 Nov, 2009

 

I'm a little confused as I can't see where the 0112 comes from at the beginning and I didn't realise that phi was associated with a number although Pi is but that is 3.142 but but the number goes on forever with a re-occuring 3.

24 Nov, 2009

 

I felt as though I was being hypnotised looking at your sunflower spirals lol !
Does it apply to lottery numbers too ;)) Fascinating stuff !

24 Nov, 2009

 

Cant say I fully understand it Wagger but must be something in it to still be referred to 600 years later ..

24 Nov, 2009

 

0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 etc, Toto. Phi is also a never-ending number which are called 'irrational mathematical constants'. Phi is used in architecture, art and design and has been in use for over 2,400 years.

24 Nov, 2009

 

What's the matter Bonkers. Can't you understand basic scientific, thrice manipulated, binery and dennery numbers simply put with the theory of relativity and put through the Hadron Collider before being sent to the wife for interpretation?

24 Nov, 2009

 

Wish it did, Aster.
Nor do I completely, Bb but still reading.

24 Nov, 2009

 

Thanks Wagger ..is that all ? You making me feel like such a dinosaur so I can go back 65 million years so there ...if I could understand all that Toto I wouldnt be spending my days waist deep in muck ..

24 Nov, 2009

 

Stick with it Bonkers it's much better than maths.

24 Nov, 2009

 

The lottery Aster is done in binary numbers zeros and dashes 0 and - look on your lottery ticket and there are dashes and spaces as that is what computers work on, it is also done on the Arabian sqaure and star signs eg 1 to 49 on the lottery numbers you chose are the number in the Arabian Square of Venus the planet is 1 to 49.

24 Nov, 2009

 

Its a lovely photo....but all those numbers....blimey...my brain is all frazzled...I'll take your word for it....lol

24 Nov, 2009

 

These sort of equations will ensure I do Toto ..algebra what was that all about and has anyone ever mentioned it since leaving school?

24 Nov, 2009

 

Yes they have Bonkersbon well the last three letters they have ha ha.

24 Nov, 2009

 

Well that's cleared that up then Morgana ! Thankyou :)

24 Nov, 2009

 

Your welcome Aster. so if you picked 49 that would be 32/16/1 =49 as it goes U for unit which would be 1 so it goes U/ 2 /4 /8 /16 /32 then the numbers are made up from these so 32 would be a dash 16 would be a dash and 1 would be a dash, the rest would be zeros as they are not used.

24 Nov, 2009

 

Fascinating - I love learning like this :-)

24 Nov, 2009

 

That was interesting :o)

24 Nov, 2009

 

Aw please MG and Hywel ..you really not helping ..you understand this ?

As for you Morgana .. I ve just noticed those three last letters .. he he but as for your number combinations well am I talking to a lottery winner ? dont tell me all those pics .. you bought Coventry didnt you ..

24 Nov, 2009

 

The reason 13 is considered unlucky, I once read, is because there were thirteen people present at The Last Supper. So does that mean 13 is only considered unlucky in countries where Christianity was the prevailing religion?
In Japan, four is considered unlucky because the Japenese word for four also means death.

24 Nov, 2009

 

I was ok with the Fibonacci series and fascinated in it applying to nature but then Morgana went and totally lost me LoL :~))))))))

24 Nov, 2009

 

No worries Morgana .. was lost before so maybe ignorance is bliss Pip.

24 Nov, 2009

 

Think I'll stay blissfull Bb then maybe my brain won't hurt LoL

24 Nov, 2009

 

If you all go to old tombs the dates are written in letters no numbers as letters abc etc derive from numbers. eg USA is 21st letter of alphabet S is the 19th and A is the 1st. 0 is not a number so rearrange 21.19.1 will be come 9.11 2001 date of the twin towers, Osama bin Laden name adds to 9.11

24 Nov, 2009

 

Hi Bonkersbon yes I do understand the fibonacci sequence - so long as I haven't had any alcohol to drink - hic!

24 Nov, 2009

 

Hi MG not being flippant really never heard of this before. Feeling pretty ignorant but then happy in that ignorance as cant get me head around it .

Oh Morgana only trouble with this theory is its often done after events and people use it to justify sequences.

My son was born on 4 / 4 at 4.44am according to Chinese should have called him Damien ..he s a nice lad really.

24 Nov, 2009

 

I would need his full name and full date of birth. by the numbers in your name the amount of numbers in your name along with date of birth all to do with dates in your life, of good and bad of what happens in your life, hence the saying when your numbers up its up.

24 Nov, 2009

 

Thanks Morgana but guess this confirms I m happy in my ignorance .. sure he would be too !

As recently become a grandfather hope you dont mind if I cherish this rather than concentrate on numerical sequences predicting their life expectancy.

24 Nov, 2009

 

No not life expectancy tell them their nature and and their character congratulations on becomming a grad dad, grad dad we love sing along every body he he

25 Nov, 2009

 

This seems like a good time to go to the pub as I'll need a few drinks before I can get my head around any of this. Fancy a Guiness Bonkers? Seems like you and me are the only dummies here.

25 Nov, 2009

 

Typical of a man go to the pub, good job your not married to my sister, she picked her husband up from the pub after he kept phoning for her to pick him up then cancelled in the end when she did, he was paraletic, so she took off in her car, angry as he had messed her about, dragging him around a gravel car park at the pub 3 times then down a main road before she noticed he had nt got in the car properly and hanging out the door, being dragged all that way shame, next day he said he was really sore, my sister said she was suprised he could feel any thing after all that drink inside him. lol

25 Nov, 2009

 

No you're not, Toto & Bb. I just scraped a pass in my Maths 'O' level - so although I've heard of all these number squences, I can't get my head round them! May I please join the dummies group?

Love the photo, though, Wagger! I''d like to add it to my favourites...cos it's mesmerising! I shall see if it's on your page.

25 Nov, 2009

 

Afraid it's not, Spritz - borrowed from a free photo site. You could copy and paste it to your photo album and add it that way.

25 Nov, 2009

 

OK - thanks, Wagger. I did take a look, and I couldn't see it.

25 Nov, 2009

 

I've put it on my photos now, Spritz - just for you!

25 Nov, 2009

 

You are and will always be welcome. As it happens maths, physics and electrical engineering science were my best subjects at school and later at college all of which are mathmatically based but I never heard of anything like this.

25 Nov, 2009

 

No one on this earth are dummies, its just every one has their own inteligence, of area, if we all were clever at the same thing who would clean the toilets, if taught most people would know in time.

25 Nov, 2009

 

Interesting but can't follow it.

25 Nov, 2009

 

Hi Wagger, yes I came across the fibonacci sequence when doing machine knitting, its a system that is used for doing rows of coloured stripes.

25 Nov, 2009

 

Now that's a new one on me, Stroller. I've only done hand knitting and enjoyed doing fairisle.

25 Nov, 2009

 

Why do so many plants grow according to/despite the well-respected Fibonnacci 'code'? Is it something to do with the amount of light an angled petal/part can receive at any one time? It's certainly got a purely physical, survival basis, and nothing whatsoever to do with anything mystical or 'weird'.

25 Nov, 2009

 

You've got it, B. The reason seems to be that this arrangement forms an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges.

25 Nov, 2009

 

Nature, eh? Which came first, the chicken or the egg???

;-)

25 Nov, 2009

 

Never could work that one out, LOL.

25 Nov, 2009

 

Sorry to disagree Morgana but there is a world of difference between learning, intelligence or skill. One supports the other but is not in itself much use alone.

25 Nov, 2009

 

The Fibonnaci code was clearly, and very intelligently/intellectually ( and learnedly ) based on what Fibonnacci observed around him in nature. If only we could all observe so closely, and with such intellectual ability, what else might natural law teach us?

25 Nov, 2009

 

Keh!

25 Nov, 2009

 

Que?????

25 Nov, 2009

 

The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. That's what I call 'observation'!

25 Nov, 2009

 

My brain hurts.

25 Nov, 2009

 

Ah, Toto!!!!!!!! Would you like to go and lie down in a darkened room?

25 Nov, 2009

 

Fibonnacci was alive at the same time as St. Francis of Assissi, if that puts his discoveries about the breeding patterns of rabbits into context...!!!!
How wonderful to have so much time!!!!

25 Nov, 2009

 

Probably to leave well alone Bscott .. quite happy for those who wish to , to intellectualise over the natural order of things but dont wish it on those of us who just happy to appreciate natural beauty as we see it without having to disect it.

25 Nov, 2009

 

I hear the voice of reason. Thanks Bonkers.

25 Nov, 2009

 

Right, BB, I'm outa here.

25 Nov, 2009

 

We can move on to rectangles and shell spirals if you like - or honeybee family trees - now they're interesting! Female bees have two parents but male bees only have one parent.

25 Nov, 2009

 

Nice to have known you all, but I've had enough.
Take care, go easy, and try not to show your intelligence TOO much! It's really not appreciated

25 Nov, 2009

 

No idea who he was Toto but assume a monk who locked himself away developing his theories and submitting them to paper.

This his greatest lesson.Once intellectuals released into the real world what do you get ?

Nurses that wont give personal care .
Firefighters and Police that cant do their jobs for health and safety reasons.
Gardeners too qualified to dig.

Nothing wrong with intelligence Bscott ..just your suggestion it somehow puts people on a higher plane and those without it are lesser for it as your last comment testifies.

25 Nov, 2009

 

I think if we get started on health and safety - there lies madness.

25 Nov, 2009

 

Apologies Wagger .. probably a bit out of my depth anyway . I ll shut up now .

25 Nov, 2009

 

And that's exactly why I'm going, BB.

25 Nov, 2009

 

Sorry to you too Bscott ...was really only trying to offer a different perspective and think it kinda sad that we cant do this as adults for fear of upsetting one another.

Debate is a healthy thing and sometimes forces us to see things we had previously not considered.Think thats what democracy was founded on .. I dont agree but will defend your right to express your views.

Sure we all entitled to that .. it only degenerates when issues are made personal.

25 Nov, 2009

 

You're the one who made it personal, BB, I was only offering an opinion.
Too late, mate...I'm out of here.
Democracy? I should coco. Thanks for the Voltaire ( misquote ), very kind of you.
Personal enough for you?

25 Nov, 2009

 

It is not sufficient to see and know a work of beauty.

We must feel and be affected by it. - Voltaire.

26 Nov, 2009

 

I took a maths 'A' level mock exam at 14 and passed my proper 'A' with 97% at 16 but I have an awful job with reading and spelling so where does that put me?

26 Nov, 2009

 

Maybe mild dyslexia - often a sign of high intelligence. See http://www.tomatis.com/English/Articles/dyslexia.htm

Dyslexia is not related to low intelligence. Dyslexia is a unique mind set that is often gifted and productive, but learns differently than other minds. In fact some of the most brilliant minds of our time have been known to have dyslexia

26 Nov, 2009

 

I wouldn't go that far Wagger but thank you for the compliment. :~)))

26 Nov, 2009

 

I wonder how we can go on with this discussion when, due to negative comments by some members, at least on member has left GoY!

26 Nov, 2009

 

While I agree with you, MG - I think that the member who has left had already removed all photographs from site earlier so appears to have been planning departure.

27 Nov, 2009

 

How sad! A good blog spoiled. Fibonacci is a reality. I don't pretend to understand the purity of the maths but better brains than I consider it accurate.
If you don't understand it, don't knock it and don't ridicule those who do!

27 Nov, 2009

 

Sorry Wagger no she left yesterday and has not removed her pix, or hadn't when I looked

Correction her pix have now gone...

27 Nov, 2009

 

I think it was caused by the cat's claws business - she put up a calm, reasoned blog and others went completely over the top and I think she felt she was being blamed. I looked and her pix were gone before her final comments on this blog. It's a great shame but everybody has freedom of choice whether to contribute to blogs or not. If I don't like something I just leave that blog, simple.

27 Nov, 2009

 

I agree that if a blog is starting to upset me on a personal level then I leave it alone

27 Nov, 2009

 

I have come to this blog a little late.....Its a very interesting subject. I think its fascinating how these things can all be explained through the use of numbers. That applies to music too.....I don't pretend to understand how people discover all this stuff but it is amazing. When I look at the sunflower pic I can see the beautiful symmatry and from playing with Spirograph when I was little I understand there is a mathmatical basis for it. However, how someone gets from looking at a flower to a mathematical equation is beyond me.
As for intelligence....being intelligent doesn't necessarily mean you are knowledgable or have common sense. I know someone with a very high IQ but he's as thick as two short planks when it comes to some things. There are also those who have very low IQs who can instantly calculate complicated mathematics in their heads....go figure.....we are all who we are and we all have are own strengths and weaknesses. That is what makes us all unique and makes the world an interesting place. :o)))

27 Nov, 2009

 

Well said, Gilli. What is a high IQ anyway? A couple of lucky guesses in the tests (which they tell you to do)can completely skew the results - I know from experience, lol. AND I have less common sense than a gnat!

27 Nov, 2009

 

Wagger you were offering to post another blog on a similar topic - look forward to reading!

27 Nov, 2009

 

That's not going to happen now, MG. Sorry.

28 Nov, 2009

 

Drat was looking forward to - maybe you could send me info as a pm?

28 Nov, 2009

 

I ticked I liked this blog right at the start but did not comment as I had nothing to contribute (complicated maths was never really my thing). So sorry you have all been up set by someone throwing their toys out of the pram. But does it mean that you will stop this interesting discussion on another blog I do hope not???

28 Nov, 2009

 

Drc726. Bscott is a good friend of mine. She has not 'thrown her toys out of the pram', she has left the site.

29 Nov, 2009

 

I have said what I think and will say no more!

29 Nov, 2009

 

If there is one more comment like that I will delete this blog tomorrow morning. I'm beginning to wish I'd never written it!

29 Nov, 2009

 

Don't blame you Wagger! Though it is a fab blog. Pity all the rudeness occurred I wanted to flag for Goypedia but don't feel able to now...

29 Nov, 2009

 

That's very much appreciated, MG. Thank you.

30 Nov, 2009

 

Wagger is there a way to delete the offensive comments so that it could go on GoYpedia?

30 Nov, 2009

 

Only if those members do it, and leave an asterisk or something. Apart from that, P&A can.

30 Nov, 2009

 

This is a fascinating, (if controversial) nature-science/mathematics that goes back way beyond Fibonacci himself. Although, generally speaking, it is little known, it has an importance in the natural world that could rank with Darwin. We should not forget that “button-down” minds ridiculed him as well! It would certainly not be out of place in Goypedia. Are we not all here to learn?

30 Nov, 2009

 

I agree Ponty - but with all the less nice posts?

30 Nov, 2009

 

Sadly, yes - why not!

30 Nov, 2009

 

Okay I've looked and can't see what we could put it under - any thoughts?

30 Nov, 2009

 

I see what you mean. There doesn't seem to be a suitable category.

30 Nov, 2009

 

We'll just have to ask for a new category then

30 Nov, 2009

 

How about 'Mysteries of Nature' ?

30 Nov, 2009

 

Can you tell me please where to find these categories?

30 Nov, 2009

 

Spritz you amaze me you are one of the first ones on GoY and new commers come suddenly and have lost you on the site you have been on for years. Perhaps under options or pedia. lol

30 Nov, 2009

 

Spritz, I was wondering that too....I did some searching and found that if you click on one of the A - Z letters at the bottom of the page, it will take you to Goypedia catagories listed under that letter. So, if you would like to look up "Roses", click on "R" and then at the top of the page there is a list of catagories under "R"....roses being one of them.
What I would like to see is a list of all the catagories we have....there must be quite a few now.

1 Dec, 2009

 

If you click on the nominate for GoYpedia button it take you to a new screen with to scroll down lists. Mysteries of nature isn't quite right this is scientific rather than mysterious.

1 Dec, 2009

 

Scientific? Nature? Still very much a mystery. That's the beauty and fascination of it.

1 Dec, 2009

 

Okay Ponty you suggested the new category to the 'boys' and then put it up :-)

1 Dec, 2009

 

Thanks, Mg.

1 Dec, 2009

 

MG, I was not the one who suggested the new category, not that it matters, but I have checked on the Goypedia listing and it is not there.

1 Dec, 2009

 

Morgana - yes, I've been a member for ages......and ages.....but changes happen, and my brain was suffering from over-load! LOL. Better to ask than have a brain explosion! :-(((((

1 Dec, 2009

 

No no brain explosion Spritz as we will lose you all together. Yes if I make a mistake, in spelling and I get pulled up I say why should I use my brain when they can do it for me hehe haha. I just let it all go over my head lol

1 Dec, 2009

 

Perhaps a suitable category would be 'botany' which would suit other blogs too? I have in mind seaburngirl's 'On closer inspection'.

1 Dec, 2009

 

that would make sense Wagger!

1 Dec, 2009

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