Origami: Art, Mathematics, or Architecture?

Dr. de Vries will present a hands-on workshop in which we will explore 3-dimensional aspects of mathematics through origami.  We will learn how to fold one simple unit or building block.  By combining many such units, we will construct a variety of beautiful, colourful geometric structures.  By doing so, we will discover properties of polyhedra and learn about symmetry.

Discovering Euler's Formula

In this workshop, Dr. de Vries guides the students in a playful exploration of polygons and polyhedra.  We will learn about the classification of polyhedra as regular, semi-regular, or other.   In small groups, students carefully examine one polyhedron model, and summarize their discoveries to the rest of the class.  Once all the information has been gathered, the class works together to develop Euler's Formula, which relates the number of surfaces, vertices, and edges in a polyhedron.  Euler's Formula is named after Euler, who first discovered the formula in 1750.  To date, every class visited has succeeded in developing this famous formula!  If time permits, students will construct polyhedra with toothpicks and marshmallows (yum).

Using Soap to Solve a Famous Math Problem

What is the shortest road that that will connect four cities, located on the four corners of a square?  Does the road have the shape of an X, an H, or a different shape altogether?  This problem is known as the Steiner problem.  Dr. de Vries will guide students to experiment with different road shapes, compare and discuss different shapes, and classify them into categories (classification is something mathematicians love to do).  To date, at least one student in every classroom visited has developed the correct solution to the Steiner problem!  At the end of the presentation, we will play with soap solutions, and take advantage of the properties of soap films to construct solutions to the Steiner problem.

Fractal Cards

Students investigate and create fractal cards, which are eye-catching pop-up cards with fractal properties, obtained through iterative processes.

Kaleidocycles

Students create kaleidocycles, which are rings of connected tetrahedra.  The ring can be twisted continuously inwards or outwards to show different sides of the tetrahedra.  Students are challenged to figure out ways to colour the sides of the tetrahedra to illustrate properties of symmetry.

The Tessellations of M.C. Escher

The artist MC Escher (1898 - 1972) is well known for using tessellations in his work.  His intricate tessellations of birds, fish, and reptiles are based on transformations of polygons such as triangles, quadrilaterals, and hexagons.  Dr. de Vries will guide students in their exploration of Escher's artwork to discover how he did it, and lead students through a series of exercises to create their own artwork

DNA, Knots, and Knot Theory

There are enzymes that convert rings of DNA from one topological form to another, linking them, and even tying them into knots.  It is believed that the enzymes take part in genetic replication and transcription.  Learn how the mathematical theory of knots is used to decude how the enzymes tangle and disentangle DNA.