Happy new year / Godt nytår! I hope December has been good to everyone, mine certainly has. There are lots of really cute Christmas traditions in Denmark, and I love them all: æbleskiver, Christmas lunches, dancing around the Christmas tree, the list just goes on and on. But my absolute favourite tradition this time of year is the crafting of julehjerter (Christmas hearts). They are made by braiding two pieces of paper together to form a heart, and you can make all kinds of designs appear in them. Traditional designs include stars, angels, or just a block pattern as shown in the picture below.
But you can make far more interesting designs appear in the hearts. I found some amazing patterns on the website https://flettedehjerter.dk/. Here is a picture of the hedgehog and wolf I made from their templates.
Sadly I couldn’t find any maths-related designs on internet. This is obviously a great omission, which I decided to rectify by designing my own julehjerter. But when I asked my Danish friends how to make your own designs, they didn’t know! Luckily it wasn’t too difficult to figure out how the patterns from flettedehjerter work, so I was able to reverse-engineer the process. And this is the result! I made an image of Pythagoras’s theorem and an infinity symbol.
Pythagoras’s theorem is for most people their first encounter with a mathematical proof. It also consists of easy straight lines so it was it perfect for trying out the design process. But as some of my friends remarked, it is not a particularly OCD friendly design. My second attempt, the infinity symbol, looks a lot better in comparison. I chose this design because my favourite mathematical theorem of all time is Cantor’s diagonal argument. It proves that some infinities are bigger than others, which is absolutely mind-blowing. The proof itself is simple enough to understand. Here is a great Youtube video by UndefinedBehavior explaining the proof using infinite rows of Pokemon, go have a look!
I want to write up a full explanation of how I made my julehjerter designs and teach you how you can make your own, but explaining the process step-by-step with clear illustrations takes more time than I had these Christmas holidays, so this will be a hobby project that I’ll work on every now and then in 2022, to have it ready for next Christmas. Stay tuned!