The thesis consisted of a series of paintings in which the canvases were individually painted in a predetermined way, then arranged and assembled more spontaneously in a final wall construction. Narrow limitations, such as working with only horizontal and vertical compositions and contrasting colors were specified. By working within a method or procedure, and by remaining strict to these guidelines, the ideas inherent in the paintings emerged and were then promoted. The dominant ideas that developed out of the process of making the paintings were the use of both "found" shapes -found in leftover lengths of support material-and "found" means of dividing the canvas, found in statistical information culled from current events in the newspaper. Also, the idea of unifying the painting with contrasting shapes, colors, surfaces, and values arose out of the process. The actual results of the painting process became clearer during the "spontaneous assembling of the paintings." The final wall constructions were made by arranging the individual canvases in different configurations and then mounting them on the wall. After the paintings went to the wall, possibilities for alteration and how they interacted with the wall could be seen.

Let’s expand the capabilities of Karnaugh maps to combine more than just two rows of the truth table into a single product.

Typescript. Includes bibliographical references.

In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.

This thesis consists of two main chapters along with an introduction andconclusion. In the introduction, we address the inspiration for the thesis, whichoriginates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address the case where the starting and ending points for the passage are both on the boundary. We find the possible optimal paths, and also determine the conditions under which we travel along each path. Next we move the starting point to a location outside the boundary. While we are not able to determine the exact optimal path, we do arrive at some conclusions about what does not constitute the optimal path. In the second chapter, we alter this problem to address a rectangular enclosed boundary, which we refer to as a swimming pool. The variations in this scenario prove complex enough that we focus on the case where both starting and ending points are on the boundary. We start by considering starting and ending points on adjacent sides of the rectangle. We identify three possibilities for the fastest path, and are able to identify the conditions that will make each path optimal. We then address the case where the points are on opposite sides of the pool. We identify the possible paths for a minimum time and once again ascertain the conditions that make each path optimal. We conclude by briefly designating some other scenarios that we began to investigate, but were not able to explore in depth. They promise insightful results, and we hope to be able to address them in the future.