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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