Surprising New 3-D Forms From Flat Curved Shapes
"The shapes are a beautiful representation of the integration of mathematics and art, an idea both engaging and challenging." Mathematics Teacher, NCTM Jan 2011
Surprising new 3D forms from flat curved shapes. Could you make your own Squaricle, 3-Dform, Wobbler and Twisted Bean yourself?
Developable Surfaces such as these are made from a single sheet. There are ten models that introduce D-Forms, as well as explanatory material to develop your understanding. Templates are also provided to explore ellipses with different aspect ratios, but all one perimeter. Such explorations provide fascinating projects for mathematicians, designers, artists and paper engineers.
"The basic idea, though simple, seems to be rather novel. It is not addressed by the standard mathematics or modelling literature. Apparently, there are no known closed form solutions that will predict what 3D shape will result when simple 2D figures are joined at their perimeter into a D-Form - raising a challenge for some serious mathematical research....Fortunately no math or computer is required to build all of the D-Forms in this book....[just] good, educational entertainment." Carlo H Sequin, Journal of Mathematics and the Arts vol 3, no 4.
For Teachers Mathematics Teacher, NCTM Jan 2011 comments "Classroom teachers can quickly implement D-forms using the models included in the book. The hands-on activities will help students understand simple geometrical terms (length, perimeter, two-dimensional shapes, and three dimensional figures). However, the greatest benefit of the activity is the potential to strengthen visual spatial skills."