On the first day of Christmas, my true love gave to me… some mildly interesting combinatorics! The Twelve Days of Christmas is a Christmas favourite, and whether you interpret the lyrics to mean that each day only one type of present is given, or more literally to mean that on each day you are given… Read more »

# Aperiodvent, Day 8: The Problems With Secret Santa

Enjoy a wonderful 11 minutes of @FryRSquared talking about the probability problems associated with assigning Secret Santa presents by drawing names from a hat: This post is part of the Aperiodical’s 2018 Aperiodvent Calendar.

# Aperiodvent, Day 7: Parabolic Sewing

By stitching carefully between a set of points, you can create a parabola – these Christmas cards have taken this idea and given it a festive twist.

# Aperiodvent, Day 6: Hexagonal Snowflakes

Six is the number of sides on a hexagon, and hexagonal symmetry is one of the most wintry symmetries – due to the bond angle of water when frozen into ice, all snowflakes (with some minor exceptions) have hexagonal symmetry.

# Aperiodvent, Day 5: Dodecorations

If you’re thinking about decorating your house for the festive season, we recommend the Twelve Pentagons of Christmas – dodecahedrons. Here’s a few ways to get more regular twelve-sided polyhedra into your life.

# LaTeX/TikZ to draw a star graph $K_{1,n}$

For a diagram for a class this week, I’ve written a LaTeX command to draw star graphs using TikZ. A star graph $K_{1,n}$ is a graph with a single central node, $n$ radial nodes, and $n$ edges connecting the central node to each radial node. I am sharing this here in case it is useful… Read more »

# Aperiodvent, Day 4: Möbius Paper Chains

If you’re trying to think of ways to decorate your home, office or classroom, look no further than mathematically non-trivial paper chains, made from Möbius bands. All you need is some double-sided coloured paper (ideally the same colour on both sides, but if you want to show off the twist, you can go two-tone) cut… Read more »