GOLDEN RATIO

GOLDEN RATIO

  • By
  • On 18th March 2015

Mona Lisa conforms to it.  So does Michelangelo’s David.  And so does “The Creation of Adam” on the famous ceiling of the Sistene Chapel.  These are, the scholars enlighten us, the very best works of art in the world because of the Golden Ratio.  That is precisely what makes them so beautiful, so owe-inspiring and so memorable.  Golden Ratio? Really?

Much has  been said about the use of the Golden Ratio (Sectio Aurea) in design, architecture, nature, works of art, etc. And much praise has been given and odes sung.  It has even been called the Divine Proportion.  The learned professors have found it in the Great Pyramid of Giza, the Acropolis, Taj Mahal, the Eiffel Tower, the Aston Martin cars, Salvador Dali’s paintings, and even in TOYOTA’s logo.  They tell us, “Any thing that has the golden ratio is perceived as aesthetically pleasing.  Such is the nature of the human brain“.

The golden ratio has fascinated philosophers, mathematicians, theologians and emperors for thousands of years and many books have been written on this subject exclusively.  But, what is it?

The golden ratio can be defined this way: A line divided in two sections in such a way that the whole line is to the longer section as the longer section is to the shorter section.  What?  Say that again, please.  The whole is to the longer as the longer is to the shorter.  Weird, isn’t it?  Let’s try one more time.  Split a line in two and you’ll get a long section and a short section.  Now, if you divide the length of the whole line by the length of the long section, you’ll get a number.  Let’s call it X.  Then, divide the length of the long section by the length of the short section and you’ll get another number.  Let’s call it Y.  In all cases, except one and one only, X will be different from Y.  But when X = Y, then, boy, oh boy, do we have something really special.  Little wonder some called it the Divine Ratio.  Wikipedia (Sectio Aurea) gives a very good illustration and much additional explanation.

For our purposes, all we need here is the number itself.  The magic “golden” number when X = Y.  Care to take a guess?  No, it’s not 2.  And it is not 7 either.  It is 1.61803398875…., which is an “irrational” number, like π.

Obviously, every line has a golden ratio point. Let’s call it the reference point.  Easy to find and easy to deal with, if you are looking at a line.  But what about a more complex form or object?  Especially one irregular in shape?  Well, it’s not easy to do that objectively.  In evaluating a three-dimensional multi-faceted object such as a motorcycle, for example, choosing such a reference point is purely arbitrary.

A popular consensus in evaluating motorcycles for the presence of the golden ratio is to use the “juncture” between the seat and tank as the reference point.  If the distance from this juncture to the front end and the distance from the juncture to the back end are in the golden ratio,…bingo!  The bike is perfect, they claim.  According to the above definition, BLACKSQUARE is exactly at the golden ratio as we can see from the image below.

GOLDEN RATIO SIDE VIEW BIG RED NUMBERS

 

83.5/51.6 = 1.618

51.6/31.9 = 1.618

Another popular consensus on looking for the golden ratio in motorcycles is to compare the tank height to the seat height.  BLACKSQUARE meets this criterion as well as demonstrated below.

GOLDEN RATIO TANK HEIGHT vs. SEAT HEIGHT

8.5/5.25 = 1.619

But, why stop there?  Let’s take a different look and see what else we might find.  When viewing BLACKSQUARE form behind, we discover the golden ratio present in height vs. width as shown below:

GOLDEN RATIO REAR VIEW

32/19.8 = 1.616

And we also find the golden ratio in the taillights width vs. tank width.

GOLDEN RATION TAIL LIGHTS AND TANK

17.1/10.5 = 1.628

Taking a look at the front, we see the golden ratio pop up a lot.  It is in the total height vs. wheel height.

GOLDEN RATIO FRONT WHEEL vs. HEIGHT

40.5/25.2 = 1.607

And the golden ratio is in the handle bar’s width vs. engine width.

GOLDEN RATIO FRONT HANDLEBARS vs. ENGINE WIDTH

28/17.4 = 1.609

In terms of basic shapes, the triangle shown below has a near perfect golden ratio between sides and base.

GOLDEN RATION FRONT TRIANGLE

Is BLACKSQUARE perfect then?

I prefer not to rely on numbers (however magical or golden) for the answer.  My approach to the answer is simple and, some may say, old fashioned. If it looks good, it is good.  And if it doesn’t, it isn’t.

Simple enough principle, isn’t it?  But it begs the question, “If it does look good, is this then due, at least partly, to the golden ratio?”

Not an easy question to answer.  So, let’s use the old trick: when presented with a challenge, change the subject.

A motorcycle is intended to be ridden more than it is intended to be looked at.  And if there’s pleasure in riding it, so much the better.  Because when you are sitting in the saddle and your eyes are on the road coming at you and moving underneath you at 80 MPH, the last thing you see is any of the motorcycle itself.

Ah, sorry.  Forgot about the front wheel.  It is not the original CB550 wheel, but a front wheel from a HONDA CL450.  Amazingly, it conforms to the golden ratio as seen below.  Kudos to the HONDA  designers!

FRONT WHEEL GOLDEN RATIO

 

Before closing, let’s remind ourselves that linear proportions depend on perspective.  When viewed from different angles, some of the linear golden ratios illustrated above will simply vanish.  Meaning they will no longer be “golden” at 1.618.  The image below demonstrate this well.  The perfect golden ratio, present in a direct side view, has now become almost 1 : 1.  Interestingly, other features, that were not in the golden ratio in previous views, can, now, from this particular perspective, pop into the magic of the perfect 1.618 : 1.  Fun, isn’t it?

NEW GOLDEN RATIO

 

NOTE: All dimension shown in inches were actual measurements taken using a tape measure.  Accuracy was perhaps 1/8″ or so.  In the photos showing just 1.618 and 1.0, no actual measurements were taken.  The ratio was determined using Adobe Acrobat Pro’s Measuring Tool.

QUESTIONS?