The Golden Ratio
From April 2020 to March 2021 I posted 17 blog articles looking at public library data and trends in the evolution of public libraries. On average one every three weeks. And then things went quiet. There was nothing for two months, before two articles were added in June. And then another two months before a second pair of articles in August/September. And here we are in December 2021, three months further down the track with no blog action. What happened?
Well, the good news (if you like these articles) is that I’ll be back online from the beginning of 2022. Some interesting data has emerged over the last six months – some COVID-related, some not – which provides insights on future library use, library infrastructure planning, customer service models and the role of libraries in supporting the wellbeing of individuals and communities. I’m looking forward to crunching those numbers into shape and producing something beautiful. (And for those who don’t think there is anything beautiful about data flick down to the bonus content at the end of this blog).
Which goes to prove that my absence from the blog was not about lack of material. I have a couple of started but unfinished pieces. Nor can it be that I was off travelling the world or basking in the wonders of my homeland. Even if I wanted to I couldn’t because we were in lockdown for large chunks of the year. And therein lies the problem – COVID lockdowns.
True confession. I live in Melbourne, Australia and I spent 262 days in lockdown. It sucked. Big time. 2020 was bad enough (a 43-day stretch followed by 111 days in mostly 5km lockdown), but 2021 turned out to be far worse because it was relentless and you knew that another lockdown was only one outbreak away. Coming barely a week after getting out of Lockdown 5, the snap one week Lockdown 6 that ended up lasting for 11 weeks was the final straw.
I like to think of myself as pretty stolid and resilient. Turns out I’m not. The spark and creativity went missing. Things that should have happened just didn’t. The moments of joy and inspiration had less staying power and were further apart. And there are those who did things much harder than I did – I know from personal experience.
But life goes on, and like so many others I am looking forward to better times ahead and the prospect of a new year, new hope, new challenges, new horizons.
So to all my readers – finish the year in style. Have a great Christmas. Spend time with people who matter. Stay safe.
See you next year.
BONUS CONTENT … THE GOLDEN RATIO (this is a bit mathematical but believe me, it’s worth it - just scan the pictures)
One of my life goals has been to make statistics more accessible and meaningful to the average person. Many years ago when I applied for a Rhodes Scholarship to Oxford University I spoke to the selection panel about a desire to study statistics further – not to advance the cause of theoretical statistical knowledge but to explore ways for school children and adults to be less daunted by numbers. Numbers have a place in nearly everything we do – think budgeting, cooking quantities, measuring timber, scoring a football game, stacking the pantry or shelving clothes. So why not embrace the supreme beauty in mathematics.
And nothing is more beautiful in mathematics than the golden ratio. I could write pages about this, but I promise not to bore you so I will keep this short – just three main points. If you want to know more try Wikipedia or Mr Google (the source of some of this information and the images).
Fibonacci sequence
The Fibonacci sequence is named after 11th century Italian mathematician Leonardo of Pisa, known as Fibonacci. He introduced the sequence to Western European mathematics, although it had been described centuries earlier in Indian mathematics. The Fibonacci sequence, starting with 1, is created by adding the last two numbers in the sequence to create the next number. The first 12 numbers are shown in the table below, where Fn is the nth term in the Fibonacci sequence. That is:
The first number in the sequence F1 = 1.
The second number in the sequence (F2) is the sum of the previous number (1) and the one before that (which as there wasn’t one we take as 0).
F2 = F1 + 0 = 1 + 0 = 1
The third number is the sum of the previous two numbers.
F3 = F2 + F1 = 1 + 1 = 2
And so on.
F4 = F3 + F2 = 2 + 1 = 3
F5 = F4 + F3 = 3 + 2 = 5
F6 = F5 + F4 = 5 + 3 = 8
Golden ratio
If you look at the ratio between consecutive terms in the Fibonacci sequence (column C in the table above) you will notice that these numbers get really close to one another the higher the sequence goes. So after 12 terms the ratio between the 12th term (144) and the 11th term (89) is 1.6180. The further you go the further the ratio narrows. It never actually settles on a fixed number but it does get close to 1.6180339887… . And this is a number that in mathematics is called the golden ratio (symbolised by the Greek letter phi φ).
Why the fancy name? Because in mathematics, two quantities are said to be in the golden ratio if the ratio of their sum to the larger of the two quantities is the same as the ratio between the two numbers. That is, (a + b) / a = a / b (as shown below):
The golden ratio (or ‘divine proportion’) appears frequently in geometry, art and architecture. A rectangle in these dimensions looks like a typical frame for a painting because some artists and architects believe the golden ratio makes the most pleasing and beautiful shape. The dimensions of the Parthenon in Greece demonstrate the golden ratio. Then there is the pentagram – the five-pointed star with sides of equal length. This figure is ‘divinely proportioned’ with the golden ratio appearing three times. In the diagram below: a / b = 1.618… and b / c = 1.618… and c / d = 1.618…
The golden spiral and natural beauty
Finally, if you draw a rectangle that gets progressively bigger in proportion with the numbers in the Fibonacci sequence (that is, a 1 x 1 rectangle, a 1 x 2 rectangle, a 2 x 3, a 3 x 5, a 5 x 8, etc.) the ratio of the sides approaches the golden ratio – the perfect picture frame.
If you then draw a circular arc that connects the opposite corners of the squares in the Fibonacci rectangle you get a shape called the Fibonacci or golden spiral. The golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
The golden spiral is in itself an interesting shape. But more interesting is the fact that the Fibonacci sequence and the golden spiral appear not just in mathematics (e.g. with applications in computer search techniques), but also in nature, especially biological settings such as branching in trees, the arrangement of leaves on a stem and bee ancestry. It seems the stepwise progression described by the Fibonacci sequence matches the optimal growth sequence for many plants. These dimensions allow objects to grow without changing shape, and in plants provide optimal exposure to the sun. So, for example, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, the arrangement of a pine cone's bracts and the spirals of a sunflower all demonstrate the Fibonacci sequence.
To finish, here are a couple of images from a guy who knew a thing or two about natural beauty. Leonardo Da Vinci was a brilliant mathematician and used the golden ratio and the golden spiral in his artwork. He did an entire exploration of the human body and the ratios of the lengths of various body parts – finding that even the human body is proportioned according to the golden ratio!
