Geometry at Artprize

My wife's family is very serious about Artprize.  Her parents and sister volunteer several times during the event.  My wife and daughter and I usually make two to three, if not four, trips downtown during Artprize.  The first day we went, I took our camera along, in hopes of finding some geometrically interesting art.  I had hoped to notice some geometry that was very subtle yet deeply tied to the art.  Most of what I photographed, though, was pretty obvious in its geometry.  Nothing too profound here.  And this is only from one visit, so I'm sure there were many more "geometric" entries that I never ran across.  But here are a few things that I saw.

In the Gerald R. Ford Museum, one of the entries was Reflection, by Josemiguel Perera.  Aptly named, I thought, since it has reflection symmetry across a horizontal.  I added these circles to the picture to emphasize the concentric circles in each fan.  The little circles are tangent to one another.  Of course, then the larger circles with the same centers intersect.  I thought it was interesting that connecting the points of intersection on the larger circles created a segment that passed through the point of tangency of the smaller ones.  I suppose this would be the case any time two congruent larger circles are  concentric with two smaller, congruent, externally tangent circles.  That's a fairly specific situation, though. 

I also found some of the Artprize signs interesting.  They suggest geometry at a pretty basic level, so this was no great discovery on my part - all circles, triangles, and squares.  From the right side of the sign, this pair of shapes stood out to me (right end, middle row of figures).  It's a quarter circle with an isosceles right triangle attached to the side, with legs equal to the radius of the circle.  It's divided up differently than that, though, with a long diagonal across the middle.  My drawing from GeoGebra shows three triangles, and all of them have the same area.  Each of them has the radius of the sector as its height, and half of the radius as the base (the vertical radius is bisected by the diagonal - the two line segments are diagonals of a parallelogram).  Each of the three triangles has an area of (pi*r^2)/4.  The light blue portion of the this figure (as seen in the Artprize sign) has the same area as that of a full quarter sector of the circle with this radius.  These are somewhat random musings, but it seems there is probably more in this picture that could be uncovered and might be interesting.

At another venue, someone had put together a bunch of square Artprize signs into an interesting design.  This got me thinking about squares inscribed inside one another, with vertices tangent to the midpoints of the outer squares' sides.  It's related to the special, isosceles right triangles that show up when these midpoints are connected, and square roots of 2 canceling one another out, but there was an interesting relationship in these, too.  As more inscribed squares were added, every second square would have its side length halved.  In other words, the second inscribed square would have side lengths half as large as the outermost square.  The side lengths between were, according to the special right triangle relationship, the outer square's side length times square root 2.  I thought it was interesting that every second square had half the side length (and one fourth the area).

There were some other geometric aspects of entries that caught my eye.  Silkwaves in the Grand, by Al and Laurie Roberts consisted of flags in the Grand River.  The flag poles were connected near their bases, which made it apparent that they were arranged in star formations - pentagons with triangles attached to each side.  I wonder if there was a particular aesthetic reason this arrangement was chosen.

At the B.O.B., Through the Iris, by Armin Mersmann was my favorite entry.  It was impressive to me because I thought the pictures were photographs, but they were pencil drawings!  I usually take for granted the perfect (or near perfect, considering my astigmatism) circular geometry of human eyes.  It's pretty amazing, and it was nice to be reminded of it.

Most of my geometric noticing was fairly mundane, but it was fun to spend the day being attentive to the subject in my surroundings.  Here are a few other Artprize entries that stood out as being more geometric than others:

Sacrifice, by Tom Panei

Facing Al Aquaba, by Maurice Jacobsen

Hilo - Sacred Geometry, by Kimberly Toogood

I failed to write down the exhibit name and artist for this one.
Nice to see pi in my search for geometry, but unfortunately
it was backward in every place it appeared in this exhibit.