Display Standard - Veritas et Visus

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Veritas et Visus Display Standard February 2009 De Divina Proportione The evolution of aspect ratios… 2 by Mark Fihn In the past 30 days, I’ve received four unrelated inquires about the current trend in the PC industry toward 16:9 aspect ratios as opposed to 16:10 aspect ratios. Since I’ve spent an enormous amount of time and energy over the past few years studying display-related aspect ratios, and since I was personally involved in the creation of the 16:10 aspect ratio, I decided to write a detailed article about much of what I’ve learned about aspect ratios. Aspect ratios before displays: Long before electronic displays, there was a long scientific inquiry into aspect ratios, (which simply is the width of an image divided by its height). Centuries of experimentation and scientific inquiry have come and gone to help identify the optimal sizes for many media – including paper sizes, newsprint, books, paintings, windows, etc. Different aspect ratios have emerged in different regions of the world for different needs, technologies, and usage environments. There is a long history of inquiry related to the optimal aspect ratio for the human visual system – trying to identify the best solutions for how we view images. Before we had TVs and computer monitors, visual artists spent hundreds, even thousands of years experimenting with solutions to most pleasantly put paint to canvas. Interestingly, there is a considerable amount of evidence which suggests the art world has long identified something very close to the current “wide” aspect ratio that is being largely used by both the PC and CE industry in today’s displays. The Golden Ratio: The golden ratio is often denoted by the Greek letter ϕ (phi). In simplest terms, the Golden Ratio occurs when point C divides the line in such a way that the ratio of AC to CB is equal to the ratio of AB to AC. The algebra (dating back to the time of Euclid and Pythagoras) shows that the ratio of AC to CB is equal to the irrational number 1.6180339887…(precisely half the sum of 1 and the square root of 5). Expressed algebraically, the equation has as its unique positive solution the algebraic irrational number: For at least 500 years now, physicists have suggested that the Golden Ratio translates to the most aesthetically beautiful appearance for the human visual system. A golden rectangle is a rectangle whose side lengths are in the golden ratio. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle; that is, with the same proportions as the first. Square removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. According to astrophysicist and math popularizer Mario Livio, since the publication of Luca Pacioli's De Divina Proportione, when “with Pacioli's book, the Golden Ratio started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use”. Many artists and architects have proportioned their works to approximate the form of the golden rectangle, which has been considered aesthetically pleasing. The proportions of the golden rectangle have been observed in works predating Pacioli's publication. Beginning in the Renaissance, a body of literature on the aesthetics of the golden ratio has developed. As a result, architects, artists, book designers, and others have been encouraged to use the Golden Ratio in the dimensional relationships of their works.
Veritas et Visus Display Standard February 2009 The De Divina Proportione is a three-volume work published 500 years ago – in 1509. Pacioli, a Franciscan friar, was known mostly as a mathematician, but he was also trained and keenly interested in art. De Divina Proportione explored the mathematics of the Golden Ratio. Containing illustrations of regular solids by Leonardo Da Vinci, Pacioli's longtime friend and collaborator, De Divina Proportione was a major influence on generations of artists and architects alike. Whether Leonardo proportioned his paintings according to the golden ratio has been the subject of intense debate. Salvador Dalí, on the other hand, explicitly used the Golden Ratio in his masterpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, with edges in Golden Ratio to one another, is suspended above and behind Jesus and dominates the composition. Dali’s “The Sacrament of the Last Supper” uses the Golden Ratio “The Golden Ratio has been used in many great works of art to achieve what we might term “visual effectiveness”. One of the properties contributing to such effectiveness is proportion – the size relationships of parts to one another and to the whole. The history of art shows that in the long search for an elusive canon of “perfect” proportion, on that would somehow automatically confer aesthetically pleasing qualities on all works of art, the Golden Ratio has proven to be the most enduring”. -- Mario Livio De Divina Proportione discussed φ and its uses in architecture and art. Da Vinci studied Pacioli's text, and was fascinated by φ – it ended up taking a major role in many of this sketches and paintings. In particular, his infamous “Vitruvian Man” sketch is his illustration of how the human body supposedly embodies the divine proportion φ. Once Da Vinci embraced it, artists and architects all over Europe immediately jumped on the bandwagon, and it's pretty much continued to be used by artists and architects all the way to the present. The image in the right was used early on to promote the new ATSC 16:9 aspect ratio, borrowing from the images of both Da Vinci and Dali. 3
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Display Standard - Veritas et Visus

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