Sunday, 22 January 2012

Go! Figure ...

... the Hindu-Arabic numeral system and the Fibonacci number system.

Leonardo Fibonacci  (c1170 – c1250), an Italian mathematician, as a young boy had travelled with his wealthy Italian merchant father, during which time he realised that arithmetic with Hindu-Arabic numerals was simpler and more efficient than with Roman numerals.

Copy of a Roman Abacus
He set out and travelled the Mediterranean world studying under the leading Arab mathematicians of their time, returning in 1200.  At the age of 32 he published what he had learnt in “Liber Abaci” (Book of Abacus or Book of Calculation), thereby popularising the representations we use today.

Briefly the system had been developed by Indian mathematicians in the 1st to 5th centuries AD, before being adopted by the Persian mathematicians in India and passed on to the Arabs further west.  The numeral system was transmitted to Europe in the Middle Ages, when with Fibonacci’s publication ... the use of Arabic numerals spread around the western world through European trade, books and ultimately colonisation.

Iris - Three
Delphinium - Eight
Primrose - Five

Fibonacci numbers follow an integer sequence and by definition the first two numbers in the Fibonacci sequence are 0 and 1, with each subsequent number being the sum of the previous two:

0, 1,  1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, .... as can be seen in these flower photos and their petals

Cineraria - Thirteen
Bellis Daisy, 13, 21 or 34
Chicory - Twenty One

The surprising thing perhaps, or should it be unsurprising, is that they occur naturally in biological settings, such as the branching in trees, arrangement of leaves on a stem, the fruit spouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone.

Michaelmas Daisies - 55 or 89
with Red Admiral Butterflies
The Sunflower
has 21, 34, 55, 89, or 144 clockwise
paired respectively with
34, 55, 89, 144, or 233
We have always relied on numbers – our lives depend on them -  the Roman legions used them, the Domesday book recorded them, as did the pioneers through the centuries – Archimedes, Copernicus, Galileo, Kepler, Newton, Hooke, Darwin, Einstein – while today in the UK we have the Census, which has been held every ten years since 1801.   (As a note censuses have been around for 4,000 years and been used in China, India, Ancient Israel, Egypt and even in the 15th by the Incas). 

The Core is Eden’s innovative education centre: 
see the roof and the sculpted seed below
Today engineers, scientists, mathematicians, musicians, architects, artists ... are all expanding our use and knowledge of numbers – improving on design, solar energy, lightness of materials, optimising architectural layouts, miniaturisation, et al  – there is magic in those numbers ... and in the human brain that makes use of them.

The design consists of a central hollow trunk
and roof structure reminiscent of a tree canopy. 
The central trunk houses a giant seed (right). 
The spiralling pattern of the roof is based
on the Fibonacci sequence.
There is a most beautiful short video 3.44 in the Brain Pickings post on "The Man of Numbers": Fibonacci – by Keith Devlin .. the video is stunning .. and puts to shame all my above words – what a wonderful way of explaining the Fibonacci system: enjoy.

TheTelegraph newspaper article on: A book by Keith Devlin published by Bloomsbury called “The Man of Numbers” has caused a renewed stir of popular interest.

The Eden Project in Cornwall

Hilary Melton-Butcher
Positive Letters Inspirational Stories


Joanne said...

Fascinating post, Hilary. Math has always seemed so far removed from what I do, and my thinking. I've always considered the whole realm of mathematics its own language, one I've never learned beyond the basics. And yet, though it seems removed from what I do, it's also at the very root of much of life, isn't it.

Better is Possible said...

So interesting. When I used to teach math and had kids that were math phobic, I would explain that math really is playing with numbers and patterns. We'd start the year (regardless) of grade playing with number patterns and in some cases I think it reduced that dreaded math anxiety.
BTW, thanks for leaving me a comment via Lady.

Susan Scheid said...

Oh, great post (again!). That Nature by Numbers video, which I'd first learned about at another great site, Lines and Colors, is a real beauty. Thanks for another awe-inspiring post!

Hilary Melton-Butcher said...

@ Joanne - glad you enjoyed it - the pictures highlight so much .. I agree, I used to quite enjoy maths at school but they stopped me taking it to the next level - not sure I would have made that grade BUT ...

It amazes me how much maths as we humans call it is as you say 'the very root of much of life' - so true.

@ Carol - glad you enjoyed it .. and I think I'd have liked to learn more maths with you.

Glad you got the comment - it's frustrating not being able to comment on embedded comment boxes.

@ Susan - excellent you'd seen the video "Nature by Numbers" ... it is SO GOOD. Glad you enjoyed the post ...

Cheers Joanne, Carol and Susan - have a good week ahead .. Hilary

Old Kitty said...

I love how the natural world is mathematically perfect! Maths has never been my strongest subject (I struggle horribly with simple equations) but I appreciate the logic of numbers and the beauty they create (or perhaps it's the other way round!).

I thought the clip was most relaxing to watch! Thank you!! Take care

Rosaria Williams said...

Truly inspirational!
I suddenly forgot I have math fobia!

Betsy Brock said...

what an interesting and fascinating post! And I'm not surprised that nature is so mathmatically inclined. :)

Hilary Melton-Butcher said...

@ Old Kitty - it is mathematically perfect .. and like you I can see the beautiful logic in the patterns ..

Delighted to see you watched the video clip - it as stunning.

@ Rosaria .. great to read your comment .. thank you!!

@ Betsy .. with your eye - I can imagine you'd see so much in nature .. it is just wonderful we can be shown what is there ..

Thanks so much Old Kitty, Rosaria and Betsy - enjoy your week ahead .. Cheers Hilary

E. M. Prokop said...

This is so fascinating..I am lousy at math, even though I know it is at the root of all life.. It is a part of natural as springtime..I'm a new follower, I got your name from a comment you left on someone else's post. Your blog is wonderful! Have a great week!

Patsy said...

Nature is often the best teacher!

Karen Lange said...

Very interesting! I remember learning a bit of this in school, but you make it so much more engaging. Thanks, Hilary! :)

klahanie said...

Hey Hilary,
I knew I could count on you to come up with yet another fascinating post.
I really quick at totalling numbers, 'I hasten to add'.
Cheers Hilary and I do so hope you had a peaceful weekend.
Well, that just about sums it up.....

Susan Flett Swiderski said...

It's surprising more people don't appreciate the beauty of numbers and symmetry in nature, isn't it?

Chase March said...

I never liked math as a student, but found a new passion for it in teacher's college. It really is amazing.

I really like the Fibonacci sequence. I'm not sure what exactly it is about it that captivates me.

Hope you have a great week!

Marja said...

Very interesting I didn't know the abacus is that old. Somebody ones taught me how to use it and it is quite different from what we know. I never knew about the number range in nature Absolutely amazing I always thought it was random

Hilary Melton-Butcher said...

@ Eve - nice to meet you and many thanks for the compliment. Ah - you've posed a question .. which came first nature's symmetry or springtime! Glad you enjoyed the maths post.

@ Patsy - you are so right there - nature is the best teacher.

@ Karen - I've been wanting to write this for a while .. but it is very simple - yet with the flowers one can see the maths.

@ Gary - I love your quips .. they send us off in different directions - thank you. The weekend was peaceful thankfully .. our English language is beautiful - like the Fibonacci flower petals!

@ Susan - I think a lot of people hadn't looked or thought about it .. we're losing our ability to think deeper ..

@ Chase - that's wonderful that you picked up maths in College, leading you to enjoy it - your students will love it too ... as you'll make it amusing.

I definitely don't understand maths .. but comprehend that it holds the key to so much in natural life ..

@ Marja - it is an amazingly long time ago that the abacus first appeared - at least 5,000 years ago! It was essential in early commerce and trade .. for basic computation.

Lovely to see you all - have good weeks .. cheers Hilary


Fascinating and interesting as always Hilary, you do your research well Thanks for sharing,


Nas said...

A very fascinating post. Thanks for sharing, Hilary!

Glynis Peters said...

Great post and video, Hilary!

At the age of 15 I was found to have a number dyslexia. My new maths teacher use the Fibonacci method to teach me adding up again. Thanks to both men I became a nurse and used maths on a daily basis.

The Blonde Duck said...

I think he's extraordinary!

Hilary Melton-Butcher said...

@ Yvonne - many thanks .. I like to get the posts so I at least understand what I'm trying to say - and that's not always easy!!

@ Nas - glad you enjoyed and good to see you.

@ Glynis - delighted you watched the video - so delightful isn't it.

Well certainly as you say both men clarified maths/arithmetic - well done on going on and becoming a nurse. Certainly you need calculations when nursing.

@ Blonde Duck - his abilities that long ago to clarify and decipher the workings of arithmetic and flowers - extraordinary as you say.

Thanks Yvonne, Nas, Glynis and the BD .. cheers - have good weeks .. Hilary

N. R. Williams said...

Hi Hilary
Thank you for all your kind words and thoughts in recent weeks. It means a lot to me.

Interesting that the Arabic system really started in India. It is also interesting that numbers are universal in their understanding, unlike language. There's a famous Bible story about that which I will not quote here. I'm sure you know it.


Unknown said...

I love maths, and so, of course, this post fascinated me. There is maths all around us. I have read about this in a book before but seeing all the flowers were so cool.

Hilary Melton-Butcher said...

@ Nancy .. hope you continue to improve ..

A great deal of the English language stemmed out of India too .. it is just so interesting how we find where we're at now.

I hate to say it .. I'm not sure which Bible story?! I hope I'm just being dim and not stupid ...?!

Cheers and look after yourself ..

@ Clarissa - the photos certainly brought the 'arrangements' to light and the video is brilliant - hope you had a chance to view .. but more importantly glad to hear you enjoyed the post.

Thanks Nancy and Clarissa .. good to see you ..

PS Clarissa - I have no idea why - but your comment ended up in Spam .. I don't have spam - but fortunately I'd spotted your comment and rescued it out of the folder.

Cheers to you both .. Hilary

T. Powell Coltrin said...

This is so awesome. I'm not really a math person, but ya know I see a license plate (car) and remember it for days. A phone number is with me for life.

Great stuff, Hillary!

Southpaw said...

I absolutely adore numbers and patterns - and nature. It's cool when they all come together.

Friko said...

Crikey, do you understand all this or have you done research?

My hat is off to you!

Hilary Melton-Butcher said...

@ Teresa .. yes I'm like that - but understanding it is slightly different - but I do like to try and understand.

Glad you enjoyed the post ..

@ Holly - I know you're into this stuff .. with your typographic interest. Thank you!

@ Friko - not really! but yes I've wanted to write on Fibonacci for a while - and the new book by Keith Devlin which received reviews .. and Brain Picking's review meant I could add to my own idea - with some research - while using their ideas (dare I say it!!).

What I like is being able to have my own educational journey here and can refer back often ...

Thanks Friko - appreciate that ..

Cheers Teresa, Holly and Friko - appreciate your comments - Hilary

Alex J. Cavanaugh said...

Math and numbers are one of the few truths.
And I admit I've never heard of the Fibonacci number system until today.

Susan J. Reinhardt said...

My brain is on tilt! I'm a word person. :)

Joylene Nowell Butler said...

I am inspired by your knowledge and research, Hilary. This stuff is fascinating. I think it is so awesome that I can always count on you for teaching me something interesting. I feel like bookmarking every time I read your posts. Fascinating information, really.

J.L. Campbell said...

Just the other day, my ten-year-old had to do some research on our numerical system. Didn't know about the numbers equated with flowers.

Mason Canyon said...

I am always amazed at the awesome things I learn when I visit your blog. I'm terrible at math but find this most interesting.

Thoughts in Progress

Hilary Melton-Butcher said...

@ Alex - well they both certainly affect us - even if we don't understand them. Glad I've introduced you to Fibonacci!

@ Susan - good phrase .. "my brain is on a tilt" ... I'll remember that one .. love it.

@ Joylene - what a wonderful comment .. thank you so much. Just glad to read you're inspired and thus interested ... that's the best from my point of view.

@ JL - I hope your daughter's research and my post matched up satisfactorily?

It's the systems of plants - numbers, how they interlink, etc - and realising how much of maths is all around us in every living thing.

Hope you looked at the video - your daughter would love it .. it's magic!!

@ Mason - thanks very much - I think you probably use maths more than you think .. words per page, dollars etc ... it's there all the time.

Delighted you all enjoyed the read - thanks Alex, Susan, Joylene, JL and Mason for stopping by - cheers Hilary

Rosalind Adam said...

I find the link between Fibonacci's system and the flower petals amazing. There is apparently a link between the Hebrew words of the bible and number patterns. Each Hebrew letter is also a number. I'm not explaining this very well because I don't understand it but there is a belief that the numbers indicate a deeper meaning from the script.

BK said...

Interesting post Hilary. I came across Fibonacci during my junior college Math but that time it was just purely for study; I had no idea that they occur in nature.

Melissa Ann Goodwin said...

I'm actually a big fan of numerology - there is a mysterious power to numbers that can't be overlooked! I saw your comment on Karen Walker's blog about how much we learn through our blogger friends. I certainly learn a lot when I visit you! And I love it!

Hilary Melton-Butcher said...

@ Ros .. the flowers were amazing and I definitely had to highlight them here - they came out of the Telegraph article.

I think there must be a great many linkages with numbers and one day I'd like to know more - so if you find out about the Hebrew connections .. do tell us please!

@ BK - many thanks .. I think like you I knew about Fibonacci - but like you I was just fascinated to see the connections with flora and fauna ... I look at things differently now ...

@ Melissa - I'm sure there must be so much 'history' / myth etc in numbers .. I don't know very much -

- but I found the Fibonacci connection so appealing and so easy to see - nature did it first!

Thanks very much for your comment - I've learnt so much from others, while inadvertently I've taught myself loads here .. and like you I love it! Thanks ...

Cheers Ros, BK, Melissa - fascinating thoughts ... Hilary

Anil P said...

Most interesting, the fact that nature blooms to a certain numerical rhythm.

Hilary Melton-Butcher said...

Hi Anil .. good to see you here - and glad you enjoyed the information - and as you say nature blooms to a certain numerical rhythm ..

Cheers - Hilary

Sharon K. Mayhew said...

Great post! I remember showing this to my students. :)

TALON said...

I was never a fan of mathematics, but these are the types of numbers I can relate to, Hilary :)

Hilary Melton-Butcher said...

@ Sharon .. I'm sure I was never shown this during my maths or arithmetic classes - so your students were lucky.

@ Talon .. they are beautiful aren't they - and I shall look at flowers in a new light ..

Cheers Sharon and Talon - enjoy the rest of your week .. Hilary

Theresa Milstein said...

These might be my favorite pictures you ever posted. It's amazing how so many cultures figured out their numbers, but there was variation and discussion between them.

Hilary Melton-Butcher said...

Hi Theresa .. they are just beautiful - but more so when we appreciate the petals that make them.

The world does amaze me - how disciplines have moved around the world, transposed, become used in each era - I wonder what happens next?!

Great comment - good to see you - cheers Hilary

Anonymous said...

Hi, Hilary. Enjoyed the post.

Hilary Melton-Butcher said...

Hi Susanne .. thanks - glad you were able to drop by .. cheers Hilary

dolorah said...

I'm hungry, thirsty, and starving for scenery Hilary. And now, I have to go to bed.

I know my dreams are going to be so haunting-fattening. I hope you are ashamed of yourself :)

Hilary Melton-Butcher said...

Hi Donna .. sorry about that - but hope your dreams satisfy your thirst and hunger amongst wonderful scenery .. cheers Hilary

Amy @ Soul Dipper said...

To learn what nature has to offer when she reveals herself to us puts me in awe time and again. From childhood, every discovery has held moments when I feel I've just discovered this all by myself and no one else knows! Do you think she laughs at me? :D

Hilary Melton-Butcher said...

Hi Amy - lovely to see you - I haven't forgotten you .. just haven't quite got there .. tomorrow!

No - I think Ms Nature would be absolutely delighted to know .. that someone recognises what she's doing..

.. she's allowed so many magical things to appear and keep appearing, or evolving so they can appear ..

Ms Nature is a truly awe inspiring realm of this wonderful world of hers - not ours ...

I think she would laugh with you .. and let you see more, discover unearthly secrets, share more with you .. oh she would laugh with you - definitely ... cheers Hilary said...

I loved the bit about nature's numerals. That's brilliant!
Haggis doesn't appeal, but those yummy desserts do.
Great post as always.

Hilary Melton-Butcher said...

Hi Madeleine .. glad you're feeling a little better. Nature's numerals are just so interesting .. but I quite enjoy haggis occasionally .. and as you say the yummy desert!

Thanks so much - have a good week .. Hilary

A.L. Sonnichsen said...

I read part of your post to my husband and he responded, "Many people say God must be a mathematician." :) I'd heard of Fibonacci through a children's book by John Scieszka called MATH CURSE and I had no idea what it was before then. So enlightening to read your post!

Hilary Melton-Butcher said...

Hi Amy .. I loved writing this post - and it's very possible God is a mathematician .. along with a few other disciplines I think! Polymath master at the very least ...

I'd heard the name - so I was pleased to be able to write a very simplified post about him and his code.

Hope you get a chance to watch the video - that is brilliant .. so good to see you - cheers Hilary

Steven Schwartzman said...

This former math teacher is glad to see you promoting the subject here. I see examples of the Fibonacci numbers and associated spirals in nature from time to time, including in the snail at

Hilary Melton-Butcher said...

Hi Steve .. great to see you here, even though not a maths teacher .. I was pleased to be able to give myself some information on Fibonacci .. and I knew other bloggers would be interested to see - a part of his code set out so simply.

I had a look at your Sepulchral White snail .. they've amazed me too when I've gazed upon them over the years.

Cheers - Hilary

Robyn Campbell said...

You have enlightened me on some things today, Hilary!

I heard of Fibonacci only from a children's story. But now I want to show this in homeschool tomorrow. It is fascinating!

I will go check out the video. Thanks, Hilary! :-)

Hilary Melton-Butcher said...

Hi Robyn .. Delighted to hear via email that you'll be discussing Fibonacci and looking at the video as part of your home-schooling today!

I've sort of done him justice by mentioning his realisation of nature's code ... bringing maths into biology ...

I agree with you it is fascinating .. we can start to see patterns of life ...

Delighted to see you here and thanks so much for visiting .. cheers Hilary

Tina said...

Takes me right back to school! I loved my math history classes, and learning how these brilliant men dicovered for example calculus (3 of them, almost simultaneously). I also enjoyed number theory very much. Would have enjoyed it more had I had a teacher who cared...
I truly love learning, and that's one of the reasons your blog is such a favorite. I always learn something here.
Thanks, Hil.
Tina @ Life is Good

Hilary Melton-Butcher said...

Hi Tina .. it's called teaching myself as I go along - and I love the learning I gather as I blog.

Gosh did you have math history .. now that must be interesting .. I wasn't very academic, but I suspect I'd have enjoyed the subject -

Thanks so much for the thumbs up re the blog ... I'm just appreciative so many seem to enjoy the blog ..

Cheers Hilary