Catalyst Project: The Construction of the Inscribed Polygonal Periodic Functions

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Catalyst Projects provide support for Historically Black Colleges and Universities to work towards establishing research capacity of faculty to strengthen science, technology, engineering and mathematics undergraduate education and research. It is expected that the award will further the faculty member's research capability, improve research and teaching at the institution, and involve undergraduate students in research experiences. This project at Clark Atlanta University will formulate the construction of the inscribed polygonal periodic functions and will provide an opportunity for undergraduate students to engage in research in mathematics. The researcher has established a strong collaboration with faculty at Pacific University.The primary goal of the research is to formulate the construction of the inscribed polygonal periodic functions. These functions have not been explored and are not documented in the literature. Specific objectives are to generalize the unit circle inscribed n-sided polygonal periodic functions and to derive properties for the inscribed square and inscribed triangle functions. Because these functionsare periodic in nature, an analysis of their behavior might provide new insight into such concepts as Fourier series, Laplace transforms, and Hilbert transforms. The educational goal is to develop active student researchers who will use multiple scientific investigative techniques and critical thinking skills to form ideas and communicate them effectively.