International postal service interruption

As of March 27th, Canada Post has suspended the ability to send shipments to a long list of countries. At this point I can still send packages to the USA and a few others. Please do not order unless your country is on the list Canada Post will ship to: https://bit.ly/2UsccNy

The Proportioner 2.0

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 use this tool to aid in designing their creations.

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)

The pentagram is replete with golden ratios; Proportioner shown atop 12.9" iPad (not included).

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. Since then, I received so many requests that I rebooted the project with a new model and second successful Kickstarter campaign, which ran in 2019.

Components of the original proportioner arrayed on a workbench in preparation for final assemblyOriginal Proportioners, from 2016 campaign (no longer available).

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 as compared to Proportioner 1.0, which is no longer in production. 

Proportioner 2.0's range is from 1-5/8" to 1'2-3/4" (41-375mm).

I 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!

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. 

People who have Proportioners sometimes use them to discover amazing things on their computer screens and in the world around them.

Proportioners shown over the spectrum of visible light and many automotive logos.The golden ratio proportions the primary colors of visible light and many automotive logos.

Additional Info

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. The Proportioner comes pre-assembled and are ready to use, right out of the box. 

Warning: Keep Proportioners away from small children. Proportioners are not toys. Proportioners have pointy ends and thin parts that can be broken if sat on or otherwise misused.

Proportioners make thoughtful gifts for the artists, scientists, intellectuals, and would-be philosophers in your life. I hope you will acquire one or a trio today and bring the golden ratio into your life and/or the lives of your loved ones!


Proportioners are available now!!

After ordering fill out the survey in the Proportioner course with your mailing address and shipping phone number.

Proportioner 2.0 – Solo

  • $33.00

    One Proportioner 2.0 with free worldwide shipping.

    Buy $44.00

Proportioner 2.0 – Duo

  • $55.00

    Two Proportioner 2.0's sent to a single address with free worldwide shipping.

    Buy $77.00

Proportioner 2.0 – Trio

  • $77.00

    Three Proportioner 2.0's sent to a single address with free worldwide shipping.

    Buy $99.00

Volume Orders

Wholesale ordering for education and retail

Get increasing discounts depending on the quantity ordered, sent in consolidated packaging. For a free custom quote, contact Scott at info@scott.training.