In our paper “Navigating Between the Dimensions”, we showed how to use classroom activities such as the Flatland Game and Creating Sliceforms as innovative and effective pedagogical strategies for engaging students in reasoning and sense making about the interplay between 2-dimensional and 3-dimensional high school geometry.  We live in the three-dimensional world of “Spaceland” but many of our means of investigation, construction and communication – on paper or monitors – are often limited to two-dimensions.   Therefore, this interplay between 2-dimensional and 3-dimensional geometry is of essential importance in many modern technological and real-life applications, such as CAT scans and medical imaging, blueprints and computer-aided design, 3D scanners and 3D printers, IMAX movies, computer animation, and virtual reality CAVES.  On this web site, we share some background information about these applications and suggest a few classroom activities that can provide an important context for the Flatland Game and Sliceform activities. 

In fact, we all play the roles of radiographers and builders each day.

Some of the applications here include areas familiar to students’ everyday lives, some will be new.  Each of them offers deep insights into the critical roles geometry plays in contemporary applications.  This illustrates how preeminent advances in modern technology build upon the ability to navigate the dimensional cycle in dynamic and quantitatively precise ways.  

You are encouraged to freely intersperse this and other material throughout your lessons.  There is certainly much to inspire our next generation of architects, engineers, artists, medical specialists, teachers, etc.