Sunday, March 2, 2014

Which one is the Golden Rectangle?

Imagine that you are floating inside the center of a very large transparent sphere, like Leonardo’s Vitruvian man above. The yellow area is our normal 60º field of undistorted view. Outside of that yellow field, things start getting weird. Our binocular vision receives two sets of images (our overlapping yellow circles in the illustration above), and sends them back to the brain for processing via the curved camera lenses of our eyes. Through comparison between these two images and a little high-speed triangulation our brains tell us how far away things are. Harry Moss Traquair described our visual field in 1927 as, "an island of vision surrounded by a sea of blindness." 

Numerous studies by “Golden Sectionists” trying to prove Man’s natural attraction towards the Golden Rectangle have found that people are just as likely to choose any horizontal rectangle that roughly conforms to the one that circumscribes the yellow shape, above [Or roughly 1:1.5, and not the Golden Ratio of 1:1.618]. 

Which one is the Golden Recatngle?

Our natural affinity for this shape is possibly its relation to our undistorted field of vision and not, after all, anything to do with nautilus shells. See if you can pick out the Golden Rectangle from the group of quadrilaterals, above. 

[I'll put the answer in the comments, below] 


  1. It's the one in the middle, top row

  2. In fact I always find the golden proportion a bit too"long" for my compositions; but as it is the "holy proportion" I try to squeeze into it...
    tks for the different approach

  3. I've rarely read a debunking of the "Golden Ratio" that was so succinct. It's certainly an interesting proportion mathematically, but I was always bothered by the claim that it is ideal or that this proportion would be singled out by the majority for its "beauty". I like your idea of the basis for our preference for rectangles (if it is yours), and since different people's eyes are different distances apart, that would be a source of variance.
    – Roger Reed

  4. I went for the middle, top row and then, after reading that people go for the 1:1,5 and not 1:1,618, though "Oh, I must be wrong - it must be the longer one, the last one in the second row" :D .

  5. They are all rectangles and they are all golden in color.

  6. you are always so clever and nice to read. thank you. Mila from Italy

  7. Another excellent post Mr. Carroll!
    Just to add to a previous comment, I don't think most find the rectangle inherently beautiful, after all a rectangle is a highly artificial construct.

    The proportion though by its nature produces internal and aggregating symmetries that relate all the elements at graduated levels. It is an excellent tool for coherence that wielded correctly, underlies many beautiful works of art and architecture.

    P.S. very perceptive Lynne :)