Sunday, January 1, 2017

The Diamond Ratio

Victory. seems to have linked to here in all seriousness. Which shows you just how shoddy a publication they are.

Disabling comments. This is a heavily linked-to post, so it attracts a lot of spam.

You have no doubt heard of the Golden Ratio, which is somehow or other connected to the Golden Mean and the Fibonacci Spiral, which is oft-touted as the basis of all great compositions. It is less likely that you have heard of the Diamond Ratio. This predates the Golden Ratio by 1000 years or more, having been first described by the Greek Philosopher Diogenes in his Disquisitiones Ultimatum dos Artes.

Socrates calls is the "Lord of Ratios", Archilochos called it the "Hero's Rectangle", and Plato refers to it constantly as the most pleasing of proportions.

Begin with a square. Inscribe within it a smaller square, rotated 45 degrees as shown. This is the Diamond.

Bisect the Diamond. This line is the Diagonal of Diogenes, who we denote with the letter R for Kalamari R. Diogenes (his full name):

Rotate the Diagonal of Diogenes around its endpoint until it is vertical. This gives the length of the long side of the Diamond Rectangle.

And finally complete the rectangle.

A little calculation gives us an approximation to the Diamond Ratio, the ratio of the sides of the Diamond Rectangle, as 1 to 1.4571. This is quite similar to our modern 3:2 ratio, the standard from 35mm film, which has been inherited by most DSLRs. Note, however, that the result is a more solid, pleasing ratio than the slightly-too-long full frame standard. Who has not looked at the standard 3:2 frame and thought to himself "nice, but I'd trim it down just a little on the long side." And so, apparently, knew the ancients just as well.

The Diamond Ratio appears throughout Art from antiquity to the modern era, of course. The pyramids. The Sphinx. The Egyptians naturally knew it. It appears in several of the important architectural features of the Parthenon, the Pantheon, and the Pantherone of ancient Greece, Rome, and Gaul.

The uses of The Eye versus The Foot in arranging things within the frame of the Diamond Rectangle is subtle, powerful, but a little too complex for the present introductory essay. Suffice it to say that The Eye shows the way toward placing the most important lightnesses and the heavier structural elements, when possible, lend themselves to The Foot of the Diamond Rectangle.

Sticking to the well known visual arts, though, here are some examples to illustrate the point. The most famous painting in the world is built on Diamond Rectangles, obviously:

And another well known painting:

It's perhaps even more blindingly clear on Botticelli's Venus:

And perhaps the clearest example of all, Leonardo's Last Supper is a textbook example of how to use it. Those skilled in the art will see near perfect utilization of the properties of The Eye and The Foot throughout.

No philosophers were harmed in the production of this helpful essay.


  1. Did someone recently stumble across that steaming pile of horse manure on petapixel where some dipstick put bollocky lines all over photographs by Mr. Ansel Adams?
    And if so, did said someone decide to humour himself and us by making an equally stupid, but stunningly funny piece of satire to see who actually believes this cobblers.
    Lastly, when will petapixel pick t up and reuse it thinking it is serious?

    Great post Andrew. After a long and very hard day here, it was just what I needed.


    1. If I can get someone to cite Kalamari R. Diogenes as an authority on composition, my time on the earth will have been well spent.

    2. Brilliant!
      I see petapixel have done it.
      Btw I love the name Kalamari R Diogenes.

  2. What, is it April already??

    Mind you, I agree with that feeling about trimming a bit off the long side of most 3:2 images... Then a bit off the short side... Then a bit more off the long side... Ending up with a square. Perfect!

    Happy New Year!


  3. Regarding it's use in Gaul, I've noticed this quite often in Asterix.

  4. Umm, are you sure it's _Kalamari_ R Diogenes - not _Kalamata_? You know, the ancient Greek nature philosopher, who also invented olives?

    Best, Thomas

  5. This piece was republished on petapixel (with permission) and the comments are, um, remarkable.

    I can give missing the Archilochus joke (he was a poet, not a philosopher) but Kalamari R. Diogenes? And HELP ME?

    This is not subtle humor!

  6. Should it not be Kalamaris?
    Couldn't stop laughing; the thought of the Petapixel Faithful having to try out the technique was just too much to bear!
    Happy New Year to you; you've certainly started in the right vein!
    Hope there's more to come!

  7. ..."Pantherone of ancient Greece"...hahaha! Well played !!
    I guess that was a pink monument, wasn't it? ��

    1. The ancients were divided, violently, over whether the Lost Pantherone of the great generals Pompey, Plutarch, and Palaver was in Greece or or Gaul.

      Everyone agrees that it was pretty great, though.

  8. I have used the Diamond Rectangle for years and just sold a print for $5m.

  9. Naughty! :)

    Noted that two other sites have picked it up from Petapixel. Can't seem to read the comments on Petapixel though, maybe they've worked it out by now!

  10. dude yer such a weirdo :) I'm going to Palm Springs.

  11. Is Diogenes related to Alexander P. Hornswoggle?

    With best regards,


  12. ... and a cup of tea, bread and jam!