Twisting the Cube: Art-Inspired Mathematical Explorations

Journal of Humanistic Mathematics

article

Bu, Lingguo¹ 

[1] Southern Illinois University Carbondale

关键词: cube;    quadric surface;    ruled surface;    twisting;    algebraic analysis;    3D modeling;   

DOI  :  10.5642/jhummath.202201.27

学科分类：社会科学、人文和艺术（综合）

来源: Claremont Center for the Mathematical Sciences

【 摘 要 】

A cube can be twisted in a playful manner for visual and algebraic insights. The twisting process and the resulting ruled surfaces can be demonstrated using 3D modeling tools (e.g., GeoGebra® and Autodesk Fusion 360®) or elastic cords on a 3D-printable scaffold. The twisted cube is aesthetically appealing, posing interesting questions that are worthwhile at multiple levels. Algebraically, the volume of the twisted cube is shown to be two-thirds of the reference cube. The twisted faces are parts of hyperbolic paraboloids, whose implicit and parametric equations can be established from diverse perspectives in support of further dynamic explorations and discussions about the surface area.

【 授权许可】

CC BY-NC-ND