# Boris Delaunay and the fashion accessories

I was wandering around the shopping mall because the power went out at my house and I happened by a store called Vera Bradley which sells fashionable bags and accessories. In the window they had on display some objects bearing one of their new patterns for 2016 called “Pop Art”.

Pop Art, to me, was absolutely stunning.

It is not only extremely reminiscent of Voronoi diagrams or Delaunay Triangulations, it is also partially symmetrical. But it’s symmetry is incredibly subtle to me… I didn’t notice it at first, part of my brain just whispered it to me. Once I saw it I was transfixed. I can’t post here of course for copyright reasons but it’s easy enough to google image search it or visit their website. Make sure you get a big example, though, like the towel or a folder or something, something big enough to demonstrate the symmetry of the pattern.

Here is an interview with the deisgner of Pop Art, Sharon Kessler:

In the interview linked above she mentions drawing upon geometric art of the past, like the 1970s… perhaps some of those old designs were using Delaunay Triangulation or Voronoi? Computers at that time were just beginning to be able to perform geometric feats such as constructing large scale Delaunay triangulations and it must have been exciting for people back then to have this brand new way to create interesting images.

But you don’t need a computer to auto calculate the shapes for you, you can draw Delaunay triangulations and paint them by hand! Here is an example of my attempt, inspired by Kessler’s design:

Here is the video of creation:

My attempt here is not as nice as Kessler’s design, which demonstrates the importance of human touch in art.

But the basic recipe is actually so simple a child could do it… you draw points, connect the dots as triangles, just make sure that no triangle is on a circle that contains any other points. It sounds complicated but there is a nice way to remember it… and it goes back to Boris Delaunay who invented it.

http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=4937&option_lang=eng

“Sur la Sphere Vide” basically means, on the empty sphere. He is basically saying… imagine you have a bunch of dots, and you draw circles through sets of three of them so that all of the circles are ’empty’, they don’t have any points inside of them. Circle, sphere, he goes to n-dimensions with his ideas.

To make it more artistic, combine a few of the triangles to polygons, so you have a tessellation of the plane with polygons. Now mirror, flip… I don’t know about anyone else but I find it fascinating.

Delaunay’s triangulation is also used in science and engineering, to for example understand the physics of space or objects in space, to take a complicated problem and think of it instead as simpler problems involving only triangles…

So to sum up. Boris Delaunay is to be found at the shopping mall. And Delaunay was a descendant of the Napoleonic invasions of Russia. So… there is time and creativity and mathematics and history and civilization…in the window display at Vera Bradley…

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This post and it’s creator are not affiliated with Vera Bradley nor Kessler in any way, shape, or form, and use of these terms do not signify endorsement nor sponsorship of any kind. Thanks for reading.