In geometry, regularity is often given great value, since it makes things simple and easily comprehensible. The symmetry and regularity of polygons tends to translate there into an aesthetic value. For this creative project, the main concept was to take an interesting 3-D shape drawn in 2-D, and change it by applying to it the idea of limits and to make it *irregular*, but still beautiful. The inspiration for this project was simply the curiosity and desire to look at and tinker with an interesting shape and take aspects of both the geometric and the calculus and mash them together into their own aesthetic fusion. Essentially, I wanted to do project synthesizing mathematical representations with the medium of embroidery, using an increasing number of stitches per sector of the structure going counter-clockwise. The desired effect was that it would slowly become more circular, the number of stitches increasing and more and more compressed in the manner of the values of a curve approaching a limit or bound.

The shape in question that I tinkered with is best described as a sort of 3-D hexagonal mobius strip, a structure that folds in on itself endlessly. In the drawing I found, it looked almost Escher-esque (we then covered Escher much later in the term), and studying it, I found that the 2-D representation, being quite hexagonal in nature, could be split up into six primary sectors. It has six arms spiraling out from the center, six inner corners, and 12 sides made up of 18 congruent lengths. To construct the sectors, then, two sides, or 3 of the congruent lengths, would comprise each sector. Taking that into account, the congruent lengths within each successive sector would each have an additional stitch than those in the last, meaning that the stitch count for the outer border would increase per sector by 3 ( (#of sector)*3= sector outer border stitch count). Using this, I overlaid a circle onto the outer border and then plotted points on the circle, split the sector of the circle for each congruent length into its allotted amount of stitches. Then, for the spiraling sections, I took the spiral that operated largely within a sector and paired them, overlaying a circle onto each one, and giving each congruent length the same number of stitches as the outer and inner borders of its sector. These would have the result of creating an increasingly circular shape going around the structure counterclockwise.

Unfortunately, the complexities of the pattern turned out less visible as I had hoped. First, I think the shape, already being hexagonal, did not leave much room for a visual comparison between angularity and circularity. Had I done this with a similar structure that was pentagonal, the results might have been more satisfyingly defined. Since the idea is to make the irregular beautiful, I had hoped to make the irregularity of its shape clear, because if it had a clear pattern, it could simultaneously be irregular and retain a sort of regularity in that pattern.

The project as a whole was a bit of a battle for visibility. I switched from white cotton fabric to painted black canvas to ensure that stitches would stand up and pop out from the embroidered medium, and had used 12-count (an homage of sorts to the recurring theme of base 6) white thread to try and bolden the outlines and raise the ends of the stitches away from each other. I wanted to make each individual stitch clearly defined and countable. I used four shades of green thread to shade the spiraling sections, trading thick 12-stranded thread for 3-stranded thread to try and keep the shaded areas (which ended up meaning a bit more than four times the stitches overall for smooth coverage). Also, I settled on green for the color of the shading after our unit on color theory, wanting to keep the color itself one of the base three, and when I had digitally prototyped the different colors, it looked much more natural than blue or red (In retrospect, this was probably subconsciously due to the existence of the wreath). Using red thread, I also made six French knot points on both the inner and outer borders of the structure to visually help separate and contain the individual sectors, twelve points in total. Despite these attempts for clarity and visibility, things ended up less defined than I would like. Working with painted canvas embroidery for the first time, I did not expect that each time a hole was poked in the canvas, the rupturing canvas would bring back up the white underside, making things messy. So, after all of this, what I seem to have created, visually, is a mathematical wreath with mathematically-placed berries. Perhaps, if we were ever able to display our works in a room on campus somewhere, we could hang it on the door.