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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Honors Theses
The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.
An Introduction To Linear Programming, Lana Sue Legrand
An Introduction To Linear Programming, Lana Sue Legrand
Honors Theses
This paper represents a study of the text An Introduction to Matrices, Vectors, and Linear Programming. It is composed chapter by chapter taking the more important statements, definitions, and theorems from each and working out exercises to illustrate their meaning. Other exercises were worked in the course of the study than are included in this paper but these were selected as brief illustrations of the type of problems that were worked.