The area of human effort known as mathematics is fascinating in the depth and breadth of coverage. The depth comes from the fact that there are so many categories of study that contain an infinite number of items; the positive integers are the simplest example. However, it is the breadth that is the most fascinating, particularly when someone invents a brand new area that can be mathematically explored. Given the simplicity of their creation, it is surprising that D-Forms have only recently been created.
By definition, a D-Form is a three-dimensional shape created when two two-dimensional shapes with the same perimeter are connected along their edges. For example, connecting an ellipse and a circle, a circle and a square or even two ellipses where their eccentricities are different. Furthermore, for objects other than a circle, using different points of initial connection can alter the final shape.
This book contains some examples of D-Forms, demonstrating what they are and how they can be created. The last 22 pages contain patterns that can be traced or cut out and then used to create the D-Forms described in the first section. Given the simplicity of the structures and the enormous range of possibilities, creating D-Forms would be an enjoyable project for elementary and middle school classes. It would also be an excellent exercise in mental modeling to take the two initial pieces and then have a class discussion over what shape the final result will be.
I can also easily create mental models of topologists poring over these figures and using them as simple objects to demonstrate principles of topology and curvature to their college level classes. Sometimes mathematics is pure and simple child’s play and that is what is described in this book.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.