Golden Ratio Box
Good as Gold
“Notice that autumn is more the season of the soul than of nature.” – Friederich Nietzsche
The Golden Ratio Box by Peter Wiltshire
Autumn is upon us again. Which means, this year, it’s time for some mathematics! Let’s contemplate ratios for a moment – specifically, when two quantities have a ratio that is equal to the ratio of their sum to the larger of the two quantities. In other words, for a>b>0, when a+b/a = a/b. Sometimes referred to as φ(phi), this ratio can be solved by the quadratic equation x2 – x – 1 = 0 and has a value of 1.618 …. (I could go on, but let’s not be irrational.) It may not be a number as familiar, famous or “easy as pi”, but phi has fame far reaching and ubiquitous throughout nature, history, art, architecture, culture and aesthetics. You might say it has a golden provenance.
There's something so pleasing about the proportions ...
This magical ratio, the “Golden Ratio”, was also the inspiration for one of the wonderful creations from Canadian cinematographer, magician and woodworker Peter Wiltshire. The box is beautifully crafted from Roasted Birdseye Maple and features ribbons of Paduak wood wrapping all around – in a perfect ratio, of course. Curly Maple lines the well hidden internal compartments (four in total), and the box requires nine to ten moves to reveal all of its secrets. The box is incredibly pleasing to look at, because the overall size, and the subsections created by the ribbon, are all proportioned in the Golden Ratio, which has been considered to be perfectly pleasing throughout the ages. The stunning choice of woods doesn’t hurt either. Peter typically likes to design his puzzles the old fashioned way, with pencil and grid paper. But for this box, he knew he wanted to incorporate the Golden Ratio exactly, so used a computer in the planning for the first time. More specifically the box is a Golden Rectangle. If such a rectangle is divided by a line into a square plus a smaller rectangle, the resultant smaller rectangle is also … a Golden Rectangle. Keep going, and going, and a Golden Spiral is created, like a nautilus shell. The puzzle box employs a highly unusual and unexpected mechanism to keep its secrets, while at the same time being an homage to the traditional Japanese puzzle box. Most who experience it find it to be … golden! Peter received a “top ten” vote award for the box at the 14th annual Nob Yoshigahara Puzzle Design Competition.
Fibonacci in Autumn by Paul MacDonald
To toast the Golden Ratio box we need to continue along the mathematical theme, and introduce another famous construct “discovered” by a thirteenth century Italian fellow with a preoccupation for rabbit reproduction. He put the theoretical sequence of rabbit population expansion down on paper, explaining how it followed a pattern where each subsequent rabbit pair would be the sum of the prior two. Starting at 1 the “Fibonacci” sequence is: 1,1,2,3,5,8,13,21 etc …. Unbeknownst to Fibonacci, this sequence is directly related to the Golden Ratio. Dividing each number in the sequence by the prior number quickly approaches a certain ratio as follows: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666…, 8/5 = 1.6, etc.. The ratio of the numbers in the Fibonacci sequence are an ever closer approximation of the Golden Ratio.
A surprising mix of diverse spirits
Whew! We deserve a drink after all that math. There was actually a point to introducing the Fibonacci sequence here, and we are getting to it now. Philadelphia mixologist and head bartender at Friday Saturday Sunday Paul MacDonald has a few claims to fame. One of them is his invention of the “Fibonacci Cocktail”. Cocktails in general rely on certain proper ratios of spirit, citrus, sweetener and modifying agents to make a well balanced drink. Ratios such a 2:1:1, 1:1:1, 8:2:1 and others are part of the canon. MacDonald thought he could extend the idea to incorporate a Fibonacci ratio, using his ingredients in a 1:1:2:3:5 proportion. It makes a lot of sense for cocktails too, and he has come up with a “number” of fantastic drinks which showcase the concept.
A beautiful array of flavors and colors, like fall foliage, in the perfect ratio
One of my favorites is his Fibonacci in Autumn, and I’ve been waiting for months to feature this drink. The time has come! The five ingredients used, in a Golden ratio, are Cocchi Americano, Cappeletti Aperitivo, Laird’s 100 Apple Brandy, Green Chartreuse and Amaro Nardini. The flavors build from lighter in flavor profile to heavier, and are balanced by cutting the volume of the richer, darker and more potent flavors as the sequence progresses. There is a lot going on here, with two Italian Amari, the intensely herbal liqueur Chartreuse, and the aromatic infused Cocchi, anchored by a sturdy apple brandy. But, as expected, it works in a harmoniously golden way. I managed to substitute a few like-minded spirits from my cabinet – Amaro Averna for the Nardini, and Meletti for the Cappeletti – and everything still worked perfectly. It’s an incredibly delicious drink, a perfect fall sip and a stunning crowd pleaser that’s sure to impress your guests. Especially if you set it all up separately and then mix it all together. Here’s to the golden days of autumn. Cheers!
I have an irrational fondness for this pair
Fibonacci in Autumn by Paul MacDonald
¼ oz Amaro Nardini
¼ oz Green Chartreuse
½ oz Laird’s 100 Apple Brandy
¾ oz Cappeletti Aperitivo
1 ¼ oz Cocchi Americano
Stir with ice and strain into a favorite glass. Garnish with a perfectly proportioned citrus spiral.
For more from this artist see:
N.B. Many thanks to AS for the use of his lovely puzzle box