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 可以生成一个新的计算机图形集合 光滑和多面体子流形的几何程序 在欧几里得3-和4-空间中。 这项正在进行的工作是 与本科生和研究生合作的结果 学生 它已被应用于提案人的研究， 分段圆曲线的几何和高度对称的 复射影平面上的组合结构。 该研究计划的初步版本已被用于 为提议者的《科学美国人》提供插图 图书馆的书和几篇文章，以及用于 数学认知周 私家侦探和他的助手们打算继续发展 这个系统，并将其应用于问题的扩展，如 以及子流形几何中的其他问题。 工作 私家侦探的数学科学界对 以及数学教育工作者。

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.