The golden ratio …

The golden ratio is an irrational number given approximately by 1.6180339887. It is one of those mystical quantities probably first mentioned by Euclid (circa 300 BCE) in his Elements. Those of you who are fond of mathematical curiosities will know of the relationship between the golden ratio and the Fibonacci sequence  (the Fibonacci sequence starts with 0 and 1 and then each subsequent entry is the sum of the preceding two – hence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …).  As the Fibonacci sequence progresses the ratio of the last two entries approaches the golden ratio. The concept is significant to me because the first numerical algorithm I ever programmed was a search procedure based on the golden ratio (called the golden section search). But the golden ratio is not just of interest to mathematicians because it also appears in nature, architecture and art. The spiral patterns of seashells and the branching of trees are related to the golden ratio. The placement of the columns of the Parthenon in Athens relative to the classical triangular upper part is reputed to be based on the golden ratio. The Mona Lisa is particularly interesting in this regard because the ratio of the length to the width of the painting is the golden ratio as is the ratio of the sides of the rectangle which is drawn to encompass Mona Lisa’s face.

So why all this preamble on a little known mathematical oddity? Well, several weeks ago now and quite out of the blue, Cath asked me if I had any suggestions for the design of a label to attach to the farm produce that we preserve. I was writing an email to one of my econometrician co-authors at the time, so I vaguely muttered something about basing a design on the golden ratio.  Cath immediately went into creative overdrive and discovered that the golden ratio is quite often used in graphic design. Apparently both Apple and Twitter used the golden proportion in designing their well-known logos. She also came up with a very elegant and catchy design for our label based on the golden spiral, which is the spiral formed by drawing a smooth curve through the opposite vertices of squares whose size is given by Fibonacci numbers. 

 

 The golden spiral

The first outing for the new label was our very first batch of cider using the juice of the Vista Bella apples we pressed earlier (see “Vista Bella day …”, posted 15 January 2024). The five litre demijohn of fermented juice ended up making 5 bottles of cider. Each bottle has a primer of sugar and pure apple juice added to it to kick start a second fermentation in the bottle and generate bubbles in the final product. At the time of writing I am happy to report that there have been no explosions. 

 

Siphoning the fermented juice into used champagne bottles

 

 

 Capping the bottles

 

 

 Adding the label

But it is not only our domestic orchard (apples and plums) that is generating excellent produce at the moment. The veggie patch is giving us generous helpings of fresh produce in the form of potatoes, tomatoes, (deformed) carrots, lettuce, zucchini and spinach not to mention the strawberries, raspberries and rhubarb. At this time of the year it becomes imperative to preserve some of the output for the lean months to come. 

 

 Proceeds picked one day last week

 

One of the successes so far has been our abundant supply of tomatoes grown in our excellent greenhouse, which still stands despite some incredibly wild, windy weather recently. We decided the best way to preserve the tomatoes was in the form of passata using a very natty tomato macerating machine. The machine takes either raw or roasted tomatoes in at the top and then passes the juice and flesh through a fine sieve and spits the pits and skin out the other side. The result is a rich tomato sauce that, when bottled and sterilised, will keep well into the winter.

Tomatoes about to be roasted

 

Separation

 The result

But life has not been all about labour recently. Last weekend we indulged ourselves by attending a electirfying performance of Rach 3 in Hobart featuring the acclaimed Korean pianist Yeol Eum Son and the Tasmanian Symphony Orchestra. It was a tour de force that had the crowd on their feet at the end. We also visited a nearby gin distillery that has developed a rather interesting activity based around creating your own blend of gin. You have at your disposal about 40 different bottles containing alcohol (vodka) infused with a single botanical (juniper, coriander, cardamom, for example) and a fact sheet containing recipes for well known gin styles (London Dry being the most famous). You then spend a happy hour crafting your own blend of gin by combining the botanicals in innovative ways.  The two bottles we created ended up smelling and tasting completely different. Cath's was described as 'refined' by our host while mine was called 'interesting'.  Aaah well, damned with faint praise once again ...

 

 

The alchemist at work