Screen Sizes with Golden Proportion

[Anders 205]

Charles Moir has published two excellent and instructive web pages, Screen Sizes, showing the common sizes with bewildering screen size acronyms, and Browser Fonts, showing all the body copy 'web safe' fonts in a variety of common sizes.

I find it particularly interesting to verify that the Wide Extended Graphics Array monitors -- Super, Ultra and Quad -- comes in the Golden Section proportion with 1.618:1 ratio.

1. WSXGA+ screen size 1680x1050, wide super;
2. WUXGA screen size 1920x1200, wide ultra;
3. WQXGA screen size 2560x1600, wide quad.

Golden Section graphic

As the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty and balance in the design of art. This is only a tool though, and not a rule, for composition.

The Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room and the table in Da Vinci's "The Last Supper" were based on the Golden Section, which was known in the Renaissance period as The Divine Proportion.

The Golden Section is a ratio based on a phi, the golden number. The Golden Section is also known as the Golden Mean, Golden Ratio and Divine Proportion. It is a ratio or proportion defined by the number Phi ( Ø = 1.618033988749895... ).

"Without mathematics there is no art", Luca Pacioli, close friend of Leonardo Da Vinci in Milan, stated in Divina proportione published in 1509. This was the first of the three books which finally made up the treatise, and it studied the Golden Ratio which is the ratio a : b = b : (a + b).

Thank you Charles for the web pages produced with Xara Web Designer.

Cheers, Anders

[zaphodeist]

Didn't realise about those screen sizes You might like to see this thread and something I cobbled together

[w00dy]

What's the odds then, on Xtreme and Charles appearing in the next Dan Browne novel?

[Burpee]

That is very interesting about the Golden Section/Ratio and screen sizes.

A wise man once told me that the ratio of 4:3 or 3:4 was easiest for computers to render in 3D art...thus 800x600 pixel images are quite common. I don't know if this really is true or not but I believed him at the time.

[Anders 205]

Pleasant to read the thread, John, and see your well made graphics. Thanks for showing.

The DNA molecule, the program for all life, is based on the Golden Section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. In 1991, Jean-Claude Perez proposed a connection between DNA base sequences and gene sequences and the Golden Ratio. Another such connection, between the Fibonacci numbers (sequence) and Golden Ratio (Ø) and Chargaff's second rule concerning the proportions of nucleobases in the human genome, was proposed in 2007.

In 2003 Weiss and Weiss came on a background of psychometric data and theoretical considerations to the conclusion that the Golden Ratio underlies the clock cycle of brain waves. In 2008 this has been empirically confirmed by a group of neurobiologists.

Cheers, Anders

[Anders 205]

You mean, Woody, Charles Moir to be a runner up replacing Dan Brown's lead character Robert Langdon in themes of cryptography, keys, symbols, codes, and conspiracy theories? Why not.

Cheers, Anders

[Anders 205]

Yes, Burpee, it is indeed. The ratio 1.618:1 has fascinated man in culture a mere 4 000 years. Certainly consciously, but mostly unconsciously.

The ratio of 4:3, that you mention, is the globally used video ratio. With more awareness of graphic harmony and balance perhaps that ratio will change in favour of the Golden Ratio.

Cheers, Anders

[zaphodeist]

Well of course, Xara starts with the Greek chi, as does christos and Charles. Moir means "big" and one of the family symbols is " ... a mort-head, with two leg-bones, in saltire proper ..." i.e. a skull-and-crossbones, beloved of the Knights Templar and Freemasons. While Gaddesden Place is already a film set so CM wouldn't have to travel far to star in the film of the book as well!

@Anders: that is what gets me! Ancient cultures may not have known about DNA, the distribution of buds on a plant's stem, etc, but they certainly realised the importance of phi. Divine geometry.

[Anders 205]

John, I certainly hold it to be true what you say about DNA in relation to Ancient culture.

Even before the beginning of these theories, some other historians and mathematicians have always proposed alternative theories for the pyramid designs that are not related to any use of the Golden Ratio, and are instead based on purely rational slopes that only approximate the Golden Ratio. Adding fuel to controversy over the architectural authorship of the Great Pyramid, Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height (4580 yrs ago), except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem nor any way to reason about irrationals such as Pi or Phi.

Michael Rice asserts that principal authorities on the history of Egyptian architecture have argued that the Egyptians were well acquainted with the Golden Ratio and that it is part of mathematics of the Pyramids, citing Giedon (1957). Historians of science have always debated whether the Egyptians had any such knowledge or not, contending rather that its appearance in an Egyptian building is the result of chance.

The Great Pyramid of Giza (constructed 2570 BC by Hemiunu) exhibits the Golden Ratio according to various pyramidologists, including Charles Funck-Hellet. John F. Pile, interior design professor and historian, has claimed that Egyptian designers sought the golden proportions without mathematical techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and everyday objects found in tombs. In his opinion, "That the Egyptians knew of it and used it seems certain."

Cheers, Anders

[philt]

You can also use the well-known Fibonacci series (1,1,2,3,5,8,..n) to approximate these proportions. Using the Xara grid you can make a scale, a thin bar for instance, marked up according to the series. I marked my bar at 2,3,5,8,13 using two different colors. It's useful because you can stretch/shrink your bar as needed while still retaining the correct proportions. For instance, say you want to divide a page vertically into three sections. Just stretch your bar the length of the page and establish guidlines as appropriate, at 3,5 and 8 say. Subdivide smaller areas? Same thing. You don't have to be slavish about this of course, but it's handy for roughing out layout. I keep the scale in my default template.

Leonardo Fibonacci, Italian mathematician (c. 1170 – c. 1250)