I was inspired by this post from Paddy MacMahon that I saw on Bluesky.
#MathsToday #ALevelMaths #FurtherMaths
Find the exact area of the snowflake.
— Paddy MacMahon (@paddymacmahon.com) December 23, 2025 at 8:19 AM
I loved that he produced this lovely snowflake from just one equation,
r = 16 + 6sin6θ + 4cos36θ. Wow!
Obviously, he knows a lot about polar coordinates, much more than I do, but that can’t keep me from playing around with his equation in Desmos and learning a little bit more in the process! All I did was replace the constant and the coefficients with sliders. My efforts produced these two snowflakes…
…and many more!
Then I thought, “What if I change the coefficients of theta?” I quickly learned that those coefficients need to be multiples of 6 to maintain the snowflake’s 6-sided shape, but yep, I’m learning from experimentation! I varied the theta coefficients over three equations to get this 3-D look:
It all makes me smile and think, “Let it snow! Let it snow! Let it snow!”
If you’re dreaming of a white Christmas, I hope you get the real thing, but if not, I hope these snowflakes will delight you at least a little bit.