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The Botanical Room part 13 - Fibonacci & 13 is my favourite number

Updated: Oct 15, 2022

13 is great,

1 plus 3 is 4 ,

which I adore,

I think I might love 8

but not




I'm proud to say that 13 is my favourite number.

We lived at number 13 when I was a little girl; they were very happy times at that house.

My lunch table at school was number 13, it was a happy table, though I rarely ate lunch.

My favourite pony at the local stables, that I would visit, and feed sugar lumps to was 13 years old.

When we moved to the country, Dad bought 13 various sheep, no idea why.

Things that I come across always seem to have 13 somewhere as a significant number.

It's also a prime number. I like prime numbers.

I don't really believe in lucky numbers or lucky anything; I just like the number 13, and I feel sorry for it being associated with unlucky Fridays etc, etc. Here we go; I am always a sucker for the underdog.

Irrespective of all its connotations, it's just a number, but it has been an important number in my life. I probably only notice it more because of my feelings for it; it is for me the most familiar of all the numbers.

13 is also one of the essential numbers within the Fibonacci series.

I love this natural phenomenon of a number sequence that repeats through nature. It is one of the few mathematical things you learn when becoming a botanical painter.

The famous "Fibonacci sequence" is 0, 1, 1, 2, 3, 5, 8, 13, 21,34,55,89…and so on, is a sequence of numbers in which each number is the sum of the previous two.

You can see this pattern throughout nature, even on our own bodies, with 2 arms, one elbow on each, 3 parts to the arm, two hands, 5 digits on each hand, and 3 sections on each finger.

You see it most clearly in plants; flowers can have 3 sepals, 5/8/13/21 petals etc often, leaves splay out in 1's or 3's or 5's.

The sequence also equates to the best way to reproduce and present at the flower head, the (generally) round seeds, each moving in Fibonacci fractions to make room for the next two and so on, creating arched patterns or if you prefer, interlocked spiral designs.

It is most visible on pine cones and in sunflower seed heads. The quantity of seed and the placement areas will be an exact Fibonacci number.

Sunflower centre photo © Billy Showell

Bee family trees are also a true example of the sequence, and the comb sections are all 5 sided and develop in the pattern of the series too.

'Honeycomb' watercolour sketch by Billy Showell

The Fibonacci series was first discovered in India but brought to attention in the west in 1202 by Pisa born mathematician Leonardo Bonacci. His name was later changed to Fibonacci, a derivation from Filius Bonacci (son of Bonacci).

If you divide any Fibonacci numbers by the one before, you will get the answer Phi or 0.618; the higher the numbers you divide, the nearer you get to Phi.

Phi is also known as the golden ratio and is used to understand and create beautiful proportions. Phi was used in classical sculpture and architecture; you may notice it in the size and proportion of the windows and doorways. Leonardo Da Vinci loved the theory of the golden ratio.

If you square up the Fibonacci numbers and place them next to one another to create a 'Golden rectangle', you get what is commonly called the golden ratio rectangle-

The combined Fibonacci squares of 1x1, 1x1, 2x2, 3x3, 5x5, and 8x8.

To find the combined area of these squares, you can add up the individual areas. Or times the height by the width of 8 x 13; this will give you the same answer; and if you divide 13 x 8, you will get Phi, 0.618 (or close as), as mentioned before, the higher you go up the series, the closer to Phi you get.

If you draw an arc from each corner of the squares to make a spiral, it will be the exact spiral shape that we see in many natural forms. Think of a shell or a succulents petals. They all form spirals that fit with the Fibonacci sequence.

Interestingly there is another sequence called the Lucas number sequence; this starts with the number 2.

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ....

Named after mathematician Francois Lucas (1842-18-91), his numbers have the same recursive pattern but start with a different value of 2. The same pattern happens, in that each number is the sum of the previous two numbers.

I read somewhere that this could be the pattern that explains plants with 4 petals and would suggest an older, simpler cell division pattern (**this could be wrong). This would maybe explain the four-petalled Fuchsias.

**Now I can't be sure without heading into more maths books and spending hours researching... I really can't be sure, but I will try to find out for another blog.

Leaves grow and develop, separated by an angle of 137.5 degrees (the radial equivalent of Phi or the golden ratio). This maximises the space and light each leaf will have. AMAZING.

Enough of the math; however, I do love a little bit of mathematics; it is a bit of common sense and order in an otherwise crazy world.

I don't often follow weird coincidences despite my love of 13 and its recurrence in my life; I know that's just silly stuff. But I like the order and understanding that a mathematical equation can bring.

I also quite like it when things are not quite exact. For instance, there are approximately 13 cycles of the moon each year; I love the word approximately.

Another nice fact about 13 is that the four seasons each have 13 weeks. So you can see there are just as many pleasant facts and wonders about 13 as there are unsettling coincidences, and we won't go there. No, we won't, it is just a number, and if you add 1 and 3 together, you get 4, and that is a lovely friendly number, isn't it?

To conclude this week, there are two memorable things I recall from when I was 13 years old.

I had my first kiss with a boy (embarrassingly under the coats in the school cloakroom at my first school disco), and mum bought me my first pair of authentic ( and really stiff) Levi jeans.

Here comes the billy poem ...


I was

Thirteen once

And loved that time

Disco Kisses under coats

Sweet, sweet memory mine

I was

thirteen years ago

That time was dear

status jeans loved and cool

'Hand me downs' within the year.

I was

Thirteen years young

Last to be chosen for the team

best thing for me, it would seem

As fielder, I could stand and dream.

I don't follow astrology, but on the Internet ( this is written about the number 13

'This number is a message of being supported by the Divine feminine energy. It announces the ending of old cycles and the beginning of new ones. It encourages you to be patient and think positive.'

I will take that as a sign. :)

'Sunflower shoe' print copyright Billy Showell available in print for my ARTforAID

Before I sign off, do check out my billyshowellfineart brand new shop; go to the top of the page to see the shop there. Look for the tags ARTforAID as those pieces will be sold to send aid for the awful crisis in Ukraine. 100% of the profit will be paid into my just giving page for each sale. I am obviously happy about any extra donations and hope to exceed the target and beyond.

I hope to be adding new paintings from my personal painting history portfolio weekly.

Wishing you peace, painting and poetry (the last one is optional) haha!

Billy x

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Bonnie A
Bonnie A
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Inspiring as always!


That was so interesting Billy, I too have long been fascinated by Fibonacci numbers and the golden ratio. Of course they pop up all over the place in nature, but also in art and other man made objects. For example Leonardo's Vitruvian Man and the 1st gen iPhone are examples of the golden ratio.

Billy Showell
Billy Showell
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Oh I knew about Leonardo’s man but didn’t know about the phones

👏🏻thanks for that little nugget ❤️


Thank you for this delightful newsletter, Billy. Fascinating information about to number 13 and Fibonacci. I'm in Australia and we're in the middle of a three day torrential downpour so this newsletter was like a ray of sunshine peeping through. I'm about to write my Autumn newsletter. It's one I write every season for my 'pumpkin' friends. It's called 'pumpkin seeds.' We're so fortunate to live in an age of technology. Love your garlic painting. It was beautiful. Cheers

Billy Showell
Billy Showell
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Hi Caroline my sister lives in Sydney and has sent vid of the rain fall, it looks biblical

not the summer you are known for at all

hope it stops soon

glad to bring a distraction however small 🤗


Jean Lee
Jean Lee
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Mathematics was my favourite subject in school so I was highly amused by your blog. Such fun. Please keep them coming.

Billy Showell
Billy Showell
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Thanks Jean, it wasn’t my favourite subject but I had moments of clarity


I love your post, I am an astronomer and like numbers. I wish you can make a tutorial of a freesia one day. Thank you!!

Billy Showell
Billy Showell
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I will add freesia to the list 😀

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