![]() ![]() You can put the vertices into a SAS data set and graph the polygon by using the POLYGON statement in PROC SGPLOT: If three vertices are on the corners of the unit square, the fourth vertex appears to be at (2/3, 1/3). You can assign coordinates to the vertices of the teal polygon. Each rotation is a different color (teal, orange, blue, and salmon) on a gray background. If the center of the pinwheel is the origin, then this pinwheel is based on a sequence of 90-degree rotations of the teal-colored polygon about the origin. Look closely at the upper left corner of "Phantom's Shadow." You will see the following pinwheel-shaped figure: A second article discusses how to use rotations and reflections to create a mathematical interpretation of Odita's painting. This article shows how to use rotations to create a pinwheel from a polygon. When I saw this artwork, it inspired me to look closely at its mathematical structure and to create my own mathematical version of the artwork in SAS. The grid displays rotations and reflections of a pinwheel shape. As I will soon explain, the image can also be viewed as 4 x 4 grid where each cell contains a four-bladed pinwheel. The image shows 64 rotations, reflections, and translations of a polygon in four colors. The artwork is beautiful, but it also contains a lot of math. Recently, a Twitter user tweeted about a painting called "Phantom’s Shadow, 2018" by the Nigerian-born artist, Odili Donald Odita.Ī modified version of the artwork is shown to the right. When I see patterns and symmetries in art, I think about a related mathematical object or process. Art evokes an emotional response in the viewer, but sometimes art also evokes a cerebral response.
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