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Full-Text Articles in Other Mathematics
Rendering Hypercomplex Fractals, Anthony Atella
Rendering Hypercomplex Fractals, Anthony Atella
Honors Projects
Fractal mathematics and geometry are useful for applications in science, engineering, and art, but acquiring the tools to explore and graph fractals can be frustrating. Tools available online have limited fractals, rendering methods, and shaders. They often fail to abstract these concepts in a reusable way. This means that multiple programs and interfaces must be learned and used to fully explore the topic. Chaos is an abstract fractal geometry rendering program created to solve this problem. This application builds off previous work done by myself and others [1] to create an extensible, abstract solution to rendering fractals. This paper covers …
Solving The Rubik's Cube Using Group Theory, Courtney Cooke
Solving The Rubik's Cube Using Group Theory, Courtney Cooke
Honors Projects
While he was working in his mother's apartment in 1974, the professor of architecture from Budapest, Erno Rubik, had no idea he was inventing one of the most popular toys in history, the Rubik's Cube. As an estimated 350 million Rubik's cubes have been sold, and approximately one in every seven people have played with one (which is about 1 billion people) it is not surprising to see that the algorithm of solving the Rubik's cube has been applied to the eld of mathematics. By using abstract algebra and more specially, group theory, the Rubik's Cube, no matter what the …