Re: Geometry in Art - Help with magazine article?

From: Scott Brown (scott_at_finebooksmagazine.com)
Date: 02/28/05 

Date: Mon, 28 Feb 2005 16:47:23 +0000 (UTC)

There are some very interesting ideas here and in the other messages on this thread. The idea of a shape composed of triangles makes some sense, as this is an allegorical painting and both a pentagram and Star of David are made up of equilateral triangles.

Thanks for all your ideas and efforts. This is great.

Scott

On 25 Feb 2005, wrote:
>I'm going to throw a few thoughts your way...but they're pretty scatty
>(you have been warned)
>
>I transformed the image as follows so I wouldn't have to keep on
>turning my head (i rotated, sheared, then used a perspective
>transformation):
>
>http://www.maths.tcd.ie/~icecube/transformed.jpg
>
>Looking at what the other guy called the disphenoid, I notice the
>following:
>
>Whatever it is, is clearly has a square base. I'm not sure what the
>shape of the front polygon is, but it looks like the one on the right
>facing away from us is four or five-sided, the top part facing us is
>two triangles, the part on the left facing left and towards us is a
>triangle
>
>actually, I don't think that's the right way to think about it- the
>transformed figure seems far more complex and ungeometrical for it to
>be intentional, and the pentagonal shape in the untransformed one is
>very apparant, but lost in the transformation...
>
>notice the star of david.
>
>The drawing on the bottom right of the page (with the triangles and
>circle) could be something to do with triangle centers, or maybe
>there's a cycloid...but I don't know enough about that sort of geometry
>to tell - you'd really have to ask someone familiar with triangle
>geometry about that one I'd guess. And I'm not familiar with the
>curves, but I don't know anything about old-fashioned constructable
>curves :( (though the one on the top centre of the rectangle curls in
>like a logarithmic spiral, as do some of the others)
>
>Actually, looking back at the original drawing, it seems it might just
>be a polyhedron with a pentagonal base (facing the woman) with around 7
>triangles connected together in some odd way.
>
>I'm almost certain it has a pentagonal base whatever about anything
>else.
>
>I though perhaps you could construct the figure by folding a star of
>david in the appropraite way...but it doesn't seem to fit together the
>right way
>
>It doesn't look like one of those ubiquitous "truncated cubes"...
>
>To my (admittedly limited) knowledge, no aritsts ever made use of
>obscure polyhedra in their drawings back then - the ones they used were
>all pretty regular.
>
>the thing on the page between the thumb and forefinger of her left hand
>looks like sperm though ;P
>
>oh, on the transformed image you can make out that the mostly-concealed
>figure on the page that the woman is keeping open is probably a
>dodecahedron.
>
>I don't know really...I'm not familiar enough with classical geometry
>to talk coherently about this stuff.

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