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 Post subject: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Mon Aug 07, 2017 1:36 pm 
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Location: Dallas, TX, USA
What is it about Darth Vader helmets and costumes that intrigue us so much?   He is the most famous villain in movie history from movies we've loved since childhood, sure.  But that still doesn't quite explain it sufficiently.  There's something about the look and shape of the helmet that just looks right, something intrisic about it that continues to captivate us and drives us to want to see and know all of its details.

I'm not an artist or a graphic designer, but those who are have learned many of the design rules and tricks to make things look appealing.  One is to incorporate the golden ratio (aka golden mean, divine ratio, aka Phi) into their designs.

    a        b
--------●-----
          G

In the line above, G is the "golden point" between the line segment of length a and the line segment of length b when the following equation is satisfied:

a/b = (a + b) / a = Phi
Phi = 1.618 (approximately, as it is an irrational number)

Exactly it is expressed as
Phi=(1+sqrt(5))/2 or
Phi=2*cos(36°)

This ratio is often seen in nature, math, and geometry. And often in company logos and at the pivot point of the arched eyebrows of cable news anchors and Congressmen.

Geometrically it can be drawn in a variety of ways.  One way is to draw a circle, then an equilateral triangle within the circle with the vertices touching the circle, and then draw a line through the midpoints of the lines of the triangle. https://www.goldennumber.net/circles

Image

Upon watching Star Wars for the 1,138,421st time, I noticed the following geometric pattern behind Darth Vader as he is interrogating Captain Antilles.

Image

Connecting a few more points of the previous diagram, we see the outline of the geometric shape painted on the wall in the background.  It appears to contain the same geometry above which is used to construct Phi.

Image

If we overlay Vader from a later scene on Tantive IV, we see that the breath mask and surrounding points on the mask match this geometry.

Image

Is this just a coincidence?  Perhaps.  In the eyes of an artist or a sculptor what "looks right" could very well match in proportion to the golden ratio.  On the other hand, this proportion may have been consciously and intentionally been specified as a design requirement. From that first scene with a close-up of Vader's helmet right next to the geometric construction of Phi in the background, it makes me think it was not just a coincidence.

We've all probably heard the conspiracy theories about certain movies being instruments of mind control (The Wizard of Oz and Star Wars in particular), or at least so compelling in their visuals that we want to watch them again and again and to unravel every detail; yet remain somewhat of a mystery why they continue to be favorites after all these years. True or false, doesn't really matter to me.

If true, all I have to say is "How long have you had these droids?..."
:wtf


Last edited by banthapoodoo on Mon Aug 14, 2017 7:35 am, edited 1 time in total.

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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Mon Aug 07, 2017 4:06 pm 
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Location: Colorado Springs, Colorado
The Golden Ratio is one of those beautiful concepts that, to me, speaks of an underlying order in nature ("Balance within the Force"). Or at least there appears to be if you measure it with triangles, lol. It's a fun idea but if it's there in the mask of Darth Vader I really think it is subliminal and not intentional, i.e. "it just looks right". Mainly because the focal point of the mask is essentially an equilateral triangle and if you put one equilateral triangle on top of another they will line up at some point.

As we know, there was no full representation of the Darth Vader mask for Brian Muir to work from, no orthographic drawings from multiple views, mainly just John Mollo's 3/4 view sketch -- which I got to see at the Denver Art Museum, it's an amazing piece of film history. The design was hashed out by John Barry and John Mollo, based on Ralph McQuarrie's concepts, and Brian Muir was left to extrapolate the concept into three dimensions. It was a perfect cohesion of artistic sensibility, training, and talent :-)


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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Tue Aug 08, 2017 1:44 am 
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Joined: Mon Mar 10, 2014 5:26 pm
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It's a fascinating number.

The average face has many instances of this ratio, as do the hand, fingers, and finger joints (phlanges, the medical term I learned after breaking a finger playing softball years ago!).

I believe Lucas and John Barry did have some minor changes they requested of Muir before approving the final sculpt. I would love to know exactly what those changes were. (Update: Barry suggested adding the tear ducts below the eyes).

A design meant to convey a sense of being organic, a creation of nature, will likely have this ratio present. If you're looking for it, you will find this ratio many many places, or something within a few percent of it, which it then becomes a matter of debate whether it was intended by design (e.g. The Great Pyramids).

The only reason I think this was intentional in this case is because of geometric pattern which is unquestionably a construction of Phi vis a vis Vader's mask in that scene. Looking at how carefully George lined up that shot, with Vader's mask profile lined up parallel to that geometric construction of Phi, keeping both in focus, I will make a leap of faith and guess as to the intent:

George was giving us a clue of Vader's duality as man and machine. The machine exterior formed by a precise forced geometry, but at his core, he was still a man, a creation of nature, not a machine or a monster.

Let me call George to see if that's the case. Anybody got his number?


Last edited by banthapoodoo on Thu Aug 24, 2017 9:06 pm, edited 1 time in total.

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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Thu Aug 10, 2017 6:05 pm 
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Here's another geometry that includes the golden mean (among other features) that overlays well onto the Vader helmet.

Image


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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Mon Aug 14, 2017 7:12 am 
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For anyone interested, there are golden mean calipers available you can use to check for the golden mean or to incorporate it into your designs.

The best I've found made by gentleman named Nick in New Zealand. He makes them for resellers but can also be purchased directly from him at http://www.goldenmeancalipers.com, which I would recommend because you have options which cases to choose from. The resellers typically only sell them with a basic polypropylene case.

I bought the small golden mean calipers with the acrylic and hardboard case shown here directly from him. The case itself is nicely designed and precision cut with laser etched text. The cover is held in place by small embedded magnets easy to remove and reattach. Cost with shipping from NZ to the US was $45. He made them to order from his shop, and I received them within a week.

Not cheap, but you get what you pay for. Elegantly designed and precise in measurement which I found to be accurate to about a tenth of a millimeter from the smallest to largest extension of the calipers. I receive no kickback or other consideration for recommending these. They are artistically designed and well made for their function by someone who cares and understands how to deliver both.

Image

Image


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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Tue Aug 22, 2017 2:50 pm 
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Truly amazing to see all this present in Star Wars among all those other things like philosophy, ancient beliefs etc.


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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Thu Aug 24, 2017 9:01 pm 
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Joined: Mon Mar 10, 2014 5:26 pm
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Indeed!

I was flipping through the book Star Wars The Complete Vader by Wyndham and Vilmur looking for drawings of cape patterns discussed in another thread.

I came across this picture of the original Star Wars Director of Photography Gil Taylor with David Prowse during shooting of Star Wars The Interactive Board Game. Set designs were reconstructed by Dick George Productions, the same company that constructed the original sets.

My attention was drawn to the wall lighting pattern, seen often in the Death Star. I thought hmmm, I wonder if... and out come the golden mean calipers.

Yep, or very close at least!

Image


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 Post subject: Re: The Golden Geometry of Darth Vader / Star Wars
PostPosted: Tue Aug 29, 2017 12:52 pm 
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Cool!


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