Interactive Computer Graphics for the Geometry of Surfaces in 3- and 4-Space

在过去的两年里，PI的NSF拨款使其有可能生成一组新的计算机图形程序，用于欧几里德3-空间和4-空间中光滑和多面体子流形的几何。这项正在进行的工作是与本科生和研究生合作的结果。它已应用于作者对分段圆曲线的几何和复射影平面上的高度对称组合结构的研究。该研究计划的初步版本已被用于为提出者的《科学美国人图书馆》一书和几篇文章提供插图，以及用于数学意识周的图像。P.I.和他的助手打算继续开发这个系统，并将其应用于问题的推广，以及子流形几何中的其他问题。P.I.的工作引起了整个数学科学界的兴趣，也引起了数学教育工作者的兴趣。

During the past two years, the PI's NSF grant has made it possible to generate a new collection of computer graphics programs for the geometry of smooth and polyhedral submanifolds in euclidean 3- and 4-space. This ongoing work has been the result of collaborations with undergraduate and graduate students. It has been applied in the proposer's research on the geometry of piecewise circular curves and on highly symmetric combinatorial structures on the complex projective plane. Preliminary versions of this research program have been used to provide the illustrations for proposer's Scientific American Library book and several articles, as well as the images used for Mathematics Awareness Week. The P.I. and his assistants intend to continue the development of this system, and to apply it to extensions of the problems, as well as other problems in the geometry of submanifolds. The work of the P.I. has interest to the mathematical Sciences community at large, as well as to mathematics educators.