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This paper is conducted to inspire the creative use and interdisciplinary assessment of parametric functions. It also attempts to articulate an infant stage of integrating media art, mathematical visualization, and the history of geometry. Throughout history, mathematicians who contributed to the study of curvature and parametric geometry were drawn to those subjects because of their inclusion of shapes reminiscent of natural forms. The Parametric Courante Project originates from the cardioid equation discovered in the 18th century.raanonguede.ga
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The Parametric Courante project tries to reframe the topic of mathematical process and organic growth to trigonometry and artificial movements. It attempts to artfully experiment with the cardioid equation by asking whether there is a geometry of sensuous visualizations. The project studies the cardioid function in the broader context of parametric equations. First, I created a series of particular mathematical visualizations that describe movements like those of an elegant baroque dancer. Through these visualizations, cardioid trigonometry and mathematical structure are explored in the environment of the computational language tool known as Processing.
This hybrid craftsmanship integrates the rationale of trigonometric functions with artful visualizations. Thus, it generates depictions of various charismatic movements using traditional cardioid patterns.
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I then quantified the artificial visualizations by their likeness to organic or metaphysical motions such as breathing, dancing, diving, soaring, loving, agitating, and so on. Explanation In mathematic structure, the cardioid equation is often expressed as:. In geometry, the expression of the cardioid equation is often a trace mark of one circle rotating around another circle with an identical radius. According to its mathematical structure and parametric geometry, I examined the cardioid equation using the following methods. Using the cardioid formula, I was able to experiment with constant 2's position and numerical value.
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This experiment determines particular frequencies as individual wave forms. A parametric geometry is identically revealed when the set of wave forms is translated from linear geometry to polar coordinates see Chart 1. However, static identical geometry does not always consist of identical frequencies. In this circumstance, constant 2 does not represent one static number as it does in the original cardioid formula.
One array is assigned by the trigonometry function cosine, labeled a; the other is associated with the sine function, labeled c. It also expresses the differences among all the geometrical movements. Artistically, Chart 2 evinces the craftsmanship of numbers and shapes. It formalizes a certain connection between digital aesthetics and parametric functions.
This method accentuates the probabilities of parametric cardioid function, transforms static patterns to "fluid" movements, and magnifies the equation's original geometry. Select what examined parameters will be used to present a complete courante dance. The processes of Method 1 and Method 2 provide visualizations, some of which appear more "natural" or familiar than others.
According to Walter Zimmerman, some visualizations can be intuited to have a certain imitation of life, while others cannot. Mathematical visualization is not math appreciation through pictures. The intuition that mathematical visualization seeks is not a vague, superficial substitute for understanding, but the kind of intuition that penetrates to the heart of an idea.
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It gives depth and meaning to understanding, serves as a reliable guide to problem solving, and inspires creative discoveries. The process of considering the results of all examined parameters fosters an internal reaction to the images, much in the same way that we synchronize with rhythm while listening to music. Thus, the equations and computer codes were selected for inclusion in the final presentation according to the seeming naturalness of their visualizations.
Each equation uses a different construction of parameter t. In Two Snow People, the time variable is associated with two values. The final crafted piece exhibits a romantic courante dance of the sine and cosine functions according to the "sheet music" of the cardioid function.
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