Saturday, August 17, 2013

Desargues and the Purple Crayon

A French professor who is about to dive into Viewpoints pointed me to an artist I'd ignored since I was a very young child (more on the "very young child below").  What do these two pictures have in common?





Well, both images show an aspect of projective (or perspective) geometry.  The first is a beautiful abstract rendering of Desargues's Theorem, which says that two triangles perspective from a point are also perspective from a line.  Here's a more boring version of the same theorem, from an article I wrote with Steph Douglas '12.


The second picture shows Harold (and his purple crayon) drawing the horizon (the image of a line at infinity) and also the images of two parallel lines, which of course meet at a point at infinity.  That's a standard image from the perspective genre.

But the pictures have something else in common:  their artist.  Here is the email that I got:

If I may, I'd like to bring to your attention, if you do not already know this, the name of the writer and painter Crockett Johnson, who authored a famous children's book Harold and the Purple Crayon, still in print. And who also, I just discovered, painted a series of paintings on mathematical subjects. You can view them on the website for the National Museum of American History at the Smithsonian. Here is the address:  
'Painting-Aligned Triangles (Desargues):
<americanhistory.si.edu/collections/search/object/nmah_694662


Wow!  So the artist who delighted in delighting me, when I was a kid, just happened to love math enough to get his own version of mathematical theorems into the nation's gallery of our shared history.  How lovely!

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