A Mathematical Approach to Obtain Isoperimetric Shapes for D-Form Construction

Ramon Roel Orduño, Nicholas Winard, Steven Bierwagen, Dylan Shell, Negar Kalantar, Alireza Borhani and Ergun Akleman
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 277–284 Regular Papers


Physical D-forms are obtained by joining the boundaries of two flat shapes with the same perimeter. To ensure both possess identical perimeters, one usually joins two pieces with identical shape (e.g., two congruent ellipses. Yet, using two different shapes increases the design possibilities significantly. In this paper, we present a simple mathematical approach to obtain two isoperimetric shapes for the physical construction of more general D-form surfaces. Using this approach, we have developed plug-ins for Adobe® Illustrator and Inkscape, which we tested in two freshmanlevel architecture studios. All of the freshman students were able to construct interesting physical D-form surfaces and then, using these physical form surfaces as casts, were able to build interesting concrete sculptures.