Catalyst Project: The Construction of the Inscribed Polygonal Periodic Functions

Catalyst项目为历史上的黑人学院和大学提供支持，以建立教师的研究能力，加强科学、技术、工程和数学本科教育和研究。预计该奖项将进一步提高教师的研究能力，提高学院的研究和教学水平，并让本科生参与研究经验。在克拉克亚特兰大大学的这个项目将形成内切多边形周期函数的构造，并将为本科生从事数学研究提供一个机会。该研究人员与太平洋大学的教师建立了牢固的合作关系。本研究的主要目的是建立内切多边形周期函数的构造。这些功能尚未被探索，也未在文献中记录。具体目标是推广单位圆内切n边多边形周期函数，并推导出内切正方形和内切三角形函数的性质。因为这些函数本质上是周期性的，对它们行为的分析可能会对傅里叶级数、拉普拉斯变换和希尔伯特变换等概念提供新的见解。教育目标是培养活跃的学生研究人员，他们将使用多种科学调查技术和批判性思维技能来形成想法并有效地交流。

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.