In high school, unit discs were all circular. Squares and diamonds were added to the list of shapes in a Real Analysis course and although more bizarre shapes appeared in graduate school, the list of possible shapes didn't appear endless. In this note, we'll show that unit discs can have almost any shape imaginable.

Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…

Directed graph theory is used to find the number of ways of building a rectangular parallelepiped from six rectangular boards using simple overlap joints. (MM)

Three illustrations of the use of Euler circuits. (MM)

Definitions and examples are given for the concepts of neighborhood, exterior, interior, and boundary points, closed and open regions, and boundedness of point sets. (DT)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

In a series of activities involving map coloring, students can discover various combinatorial theorems including Euler's formula. (SD)