The Mathematics of Doctor Who’s Fez

My oldest is a huge Doctor Who fan. She has seen all of the episodes from the last couple of seasons and quite a few of the previous ones. When Halloween started getting close she wanted to be Doctor Who, more specifically the 11th Doctor. We went to various thrift stores and department stores and outfitted her with his trade marked suspenders, tweed jacket and bow tie but the one additional think she insisted on was a fez, because to quote the Doctor “I wear a fez now. Fezzes are cool”

My husband and daughter went to several Halloween shops and even went to the address of a hat shop listed on Google, which turned out to be someone’s home, looking for a fez with no luck. So at 10pm on Halloween eve we started making one.

I’m sure you’ll be shocked to hear this but there are very few patterns for fezzes on the internet. I did manage to find one great site with a fantastic, mathematical approach to making the Doctor’s Fez over at Elinor’s Crafts. Elinor saved the day! Her instructions are great and more importantly the creation of the for a Halloween costume turned into a mini math lesson.

In order to create this fez we needed create a cone with the top cut off or a frustum as Elinor stated. To do this we needed to draw a very large cone on a very large piece of paper (which at 10pm on a Sunday we didn’t have). We improvised and taped together some sheets of newspaper and wrapping paper.

The full instructions are on Elinor’s Crafts but in short we needed to draw two lines at a 36 degree angle to each other, for this we needed a protractor, again something we didn’t have, so I printed one! (Yes you can print anything on the internet). We drew our lines and then we had to strike two arcs at different distances based on the size of her head. For this, since we didn’t have a gigantic compass, I showed her how you could use string and a pin to make an arc.