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. |

I have only been to Artprize once. My sister-in-law had entered one of her art creations. I can say that I have really never been into art. Art was never my strongest area and never really interested me. I never really thought about looking for geometry within art. I know that geometry is used in art, but never really thought about it. I guess I have never really been that invested in art. I think next year I will make an effort to go down and see Artprize. See what types of geometry I can observe there.

ReplyDeleteI thought this was a really neat entry, Matt. I know you mentioned that your observations were mundane, but I appreciated the geometric connections that you made. It is interesting that the actual Art Prize signs were comprised of geometric shapes. They must also appreciate the close ties of geometry and art. Also, thanks for posting pics! I didn't make it to Art Prize this year.

ReplyDeleteYou went to Art Prize with a purpose to find geometry. An idea like that has never dawned on me. I have also gone the last few years and had a very enjoyable time, but to include the purpose to find geometry would just make it that much more enjoyable. As I was reading your article I was retracing my steps through Art Prize this year and thinking back to if I passed anything with geometric significance. Thank you also for diving a little deeper into the pieces of art when you got home, it really enhanced the peices. Our class goes every year to A.P. I am thinking of making a little project out of this. The students are going to be in for a real treat.

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