Unique Golden Ratio Calipers

What is the Golden Ratio?

The golden ratio is a unique proportion which simultaneously patterns structures as small as DNA and as large as galaxies. 

Golden ratios are shown within DNA (left) and a spiral galaxy (right); images from my book The Divine Proportion.The golden ratio patterns very small (DNA) and very large structures (galaxies). These images are from The Divine Proportion.

I have created handheld instruments called Proportioners (in two versions, 1.0 and now 2.0) to give people the ability to discover the golden ratio in the world around themselves—and to improve whatever it is that they want to design using this amazing proportion.

Proportioner 1.0 on its magnetic stand.Proportioner 1.0 is an especially elegant instrument (shown here on its magnetic stand).

Due to its precise geometric design, the middle pointer always proportionally indicates the golden ratio with respect to the width of the outer arms.

Proportioner 1.0 open shows its connection with golden rectangleThe golden rectangle is the quintessential expression of the golden ratio in 2D.The whole is to the larger segment in exactly the same "golden ratio" as the larger segment is to the smaller. The golden ratio (~1.618), symbolized by the Greek letter Phi (Φ), is a gateway to the study of sacred geometry.

“Phi (1.618) is the most beautiful number in the universe.” -Robert Langdon, from Dan Brown’s bestselling fiction The Da Vinci Code (2003)

Proportioner 1.0 open to show its connection with a pentagram drawn on paper.The pentagram is replete with golden ratios.

The golden ratio is found in mathematics, geometry, music, philosophy, psychology, art, archaeology, architecture, geography, molecular biology, plant morphology, human physiology, physics and astronomy.

“The golden ratio is the key to universal physics.” -Sir Edward Appleton, Nobel Laureate in physics (1947)

The golden ratio isn't some rarefied or esoteric thing. It's used extensively in corporate logos and chances are you have several golden rectangles on you right now. 

Proportioner 1.0 open to show how credit card are golden rectangles (98% correlation).Credit cards are nearly perfect golden rectangles (98% correlation)

People consistently prefer designs with golden ratios without necessarily being aware of its presence or even its existence. The best designers know this proportion really works! Why not incorporate its natural power into your own designs?

Proportioner open to reveal golden rectangle geometry informing the composition of the Mona Lisa by Da VinciMy geometric analysis of Da Vinci's Mona Lisa started with the Proportioner

I wrote a book on Leonardo's hitherto unrecognized consistent use of the golden ratio in structuring his art:

book cover of Secrets In Plain Sight: Leonardo Da Vinci and the proportioner open to indicate the heart of the Vitruvian Man is at the golden ratio with respect to the circle.“Let no one who is not a mathematician read my works.” -Leonardo da Vinci

"I believe that the reason Leonardo's art has lasting power is because it is structured on the divine proportion [golden ratio]. You don't have to know anything of his very secret science to have his art move you. Seeing art structured on the divine proportion sets up a palpable resonance because the divine proportion is part of you." -from my conclusion in Secrets In Plain Sight: Leonardo Da Vinci

Enter the Proportioners

In 2016 I ran the 2000% funded Kickstarter campaign for the original Proportioner and fulfilled rewards to 543 fabulous backers. I didn't continue selling these beauties after the campaign ended because it took me an inordinate amount of time to assemble their unique compression-fit magnetic hinges, all by hand.

Components of the original proportioner arrayed on a workbench in preparation for final assemblyOriginal Proportioners in Production

Since that original campaign, I've re-designed the instrument and created the 2.0 version, which uses mechanical hinges for much more efficient assembly. The new version is larger, more rugged in the pocket & purse, and more accurate at small opening sizes. Its all-mechanical-hinge design necessitated wider arms and Proportioner 2.0 is definitely more practical, but arguably not quite as elegant as Proportioner 1.0. In a sense, Proportioner 1.0 is to Proportioner 2.0 as the Violin is to the Viola.

Proportioner 1.0 (left) and Proportioner 2.0 (right)Comparison of Proportioner models

Connoisseurs will enjoy both models. 

How to choose? So that you don't have to, I offer both models in this campaign!!

Proportioner 1.0 has a range from less than 1 inch to slightly more than 1 foot (24mm - 320mm). Proportioner 2.0 is a bit larger and ranges from 1-5/8" to 1'2-3/4" (41-375mm).

Looping animated gif showing the proportioner open and closeProportioner 1.0 indicates the golden ratio from less than 1 inch to more than 1 foot.

I am prepared for the build time in this campaign and will assemble all Proportioners by hand (parts are laser cut), and all the while I'll get to work with the golden ratio—truly a labor of love!

Each model has its unique attributes & virtues. I find that if I'm headed to the workshop or the field I tend to reach for a measure of gold in the Proportioner 2.0 but if I'm at my desk I preferentially reach for the precious jewel, the original Proportioner d'Elegance.

Proportioners showing the golden ratio with the Creation of Adam fresco by Michelangelo (left) and the fact that Saturn's rings are in a golden ratio with respect to the planet (right)Proportioners can be used to analyze anything from fine art to astrophysics.

Got the Fidgets?

I fidget with both Proportioners on my desk all the time! Watching them open and close is close-to-magical and acts as curiously soothing aesthetic therapy while you are otherwise consumed with life's stresses.

The golden ratio is such a major key to "life, the universe and everything"—the icing on the cake is that both Proportioners not only help soothe the soul but they happily occupy fidgeting hands. 

Proportioners make great classroom aids, "executive toys," stimulating conversation pieces, and superb gifts. 

The Magnetic Stand

All original Proportioners include magnetic stands laser-engraved with the golden rectangle and its classic spiral. These stands ship flat-packed as two mating parts and these require assembly. You must very firmly press the two parts of the stand together on a flat surface and optionally use any general purpose glue (not included) to bond the two parts of the stand to one another permanently. The stand will stay together without glue, but a glued joint is more solid in the long run.

The 3D model of the stand (left) and photo of assembled physical stand (right)Stands for 1.0 are backer-assembled. Press very firmly on a flat surface to fit the parts together.

Proportioner 2.0 does not come with a stand. Consider leaving it on your desk as a conversation piece or hang it on an existing nail or coat hook as a piece of art until your next use. 

If mechanical hinges loosen over time, you can easily finger-tighten their wide slotted heads. Both Proportioners 1.0 and 2.0 come pre-assembled and are ready to use, right out of the box. 

Warning: Both proportioners have sharp points and 1.0 has tiny embedded magnets that must not be liberated and swallowed. You would have to crack apart an original Proportioner to liberate its magnets but this is possible. Keep Proportioners away from small children. Proportioners are not toys.

Go to Kickstarter Campaign

Back this project to receive its rewards

The rewards in the campaign make thoughtful gifts for the intellectuals, artists, scientists, and would-be philosophers in your life. I hope you will back this project today and bring the golden ratio into your life!
Coming Soon
Proportioners 1.0 and 2.0 shown with original on magnetic stand

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