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Articles 1 - 4 of 4
Full-Text Articles in Algebraic Geometry
Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova
Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova
Journal of Humanistic Mathematics
This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!
Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo
Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo
The STEAM Journal
The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of …
Descartes Comes Out Of The Closet, Nora E. Culik
Descartes Comes Out Of The Closet, Nora E. Culik
Journal of Humanistic Mathematics
While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …
Propeller, Joel Kahn
Propeller, Joel Kahn
The STEAM Journal
This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.