Euclidean Geometry: Introduction to Tilings

Math 308

Fall 2021

This is a math class about tiling the plane. It is a beautiful subject, and I am excited to learn about it with you. When I asked my friend Elissa Ross what she thought was the best starting point was for this material, she suggested the book – a classic!Tiling & Patterns by Branko Grünbaum and G. C. Shephard. This book is full of great figures and examples that will complement our lectures. Sections of it will be required reading, and my lectures will endeavour to provide additional detail on the parts of this book that the course focusses on. As a result, this course is perhaps best thought of as "a guided reading of Tiling & Patterns."

To set an overall goal, we will set out to answer the question "what is a Penrose tiling?" An example is given in the figure on the right, which is borrowed from Non-local growth of Penrose tilings by Elissa Ross.

The course structure is undergoing an adaptation following on a fully-online version of a closely related course; click here to see this course structure in action last term. This structure enables maximum flexibility as the term evolves around the ongoing Covid 19 pandemic. The course is divided into unites and, in particular, your grade is based entirely on the homework assignments associated with each unit.

Assignment submission and grading will make use of Canvas. Here are some essential guidelines for assignment submission:

   1. Your solutions to assignments must be submitted using canvas. In particular, do not email assignments.

   2. Your solutions must be submitted as a single file.

   3. The only accepted file type is PDF.

   4. Files should be named according to the following convention:

There are free online tools available that will allow you to complete (2) and (3). Due to the volume of data being managed this term, it is really important that these 4 points be met so that we can grade your work effectively. As a result, if one (or more) of these four points are not met, your assignment will not be accepted/graded.

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              Homework assignments

              Course Units