Doctor, Doctor!

Cuddly, and apparently very drunk, penguin wearing a red fez.
The author wishes to thank Wilfred the Penguin for modelling the fez.

I'm not a Whovian, in particular. I used to watch it as a child in the Jon Pertwee/Tom Baker days, and both of them were very good, and I can't even remember who took over from Tom Baker but I rather lost interest after that. (Tom Baker, incidentally, once threw a BBC breakfast at Paul Darrow, who played Avon in Blake's 7 and who may well get a further mention in these pages at some point. The reason for this is lost to history, but I for one am glad he missed.)

But I do recall that one of the Doctors had a fez, because people kept going on about it at the time; and there was at least one person who wanted to know how to make their own, and I thought... that can't be hard. So I did this.

Large sheet of paper with the angle drawn on the left and the arms extending to the two right corners.
I drew an angle of 36 degrees on a large sheet of paper.

There was a reason for the choice of angle. It would not only provide the right slope, but it would make it very easy to calculate where the lines should go, because it is one tenth of a full circle.

Red velour hat, upside down, with a double arrow indicating the diameter.
Then I measured the diameter of a well-fitting hat.

Let's say your diameter is 25 cm. Then you're going to need an arc which is pi x 25 cm long for the circumference of the base of your fez, and if that's one tenth of a circle, then the full circle has a circumference of pi x 25 x 10 cm. You don't need to do that multiplication, because your pi is about to cancel; what you need to know is the radius of your arc. And the circumference is 2 x pi x the radius, so to get the radius you divide by (2 x pi), leaving you with 25 x 5 cm, which is 125 cm. That cancellation trick works for any diameter you want to use - the radius for the arc is always exactly 5 x the original diameter of your hat. Very nice and neat, but to make a fez that fits you, you're going to want a really huge sheet of paper; so I decided to illustrate the technique by making a smaller one to fit Wilfred the Tipsy Penguin. The wonderful thing about this method is that it scales to any size... provided you have enough paper.

The same angle, with an arc drawn across it.
Arc drawn to fit Wilfred.

Then you decide on the height of your fez, measure that distance towards the angle, make a mark at that distance on both sides, and draw another arc for the top of the fez.

A second arc drawn, with the area between them shown in green.
The green area shown is now your main pattern piece (minus seam allowances).

Trace that, add your seam allowances, and then you have a choice: you can either calculate the exact length of the shorter arc to as many decimal places as you want (which is not hard to do, but you need to be comfortable with basic circle maths), or you can just measure it. The latter, if you're careful, should give you a good enough estimate. Either way, divide your result by (2 x pi) to get the radius of the circular piece that forms the top of the fez, draw that circle, and, again, add an appropriate seam allowance. That, or you can be really clever, measure from the point of the angle to the shorter arc, and divide that measurement by 10 to get the radius of the upper circle. That will work, but if you don't know why it works, you might well be more comfortable just getting your calculator out.

The pattern drawn on tracing paper with seam allowances added.
I can't remember why I drew two circles with different seam allowances.

I used red felt and lined it. To give the fez stiffness, I just cut a piece of thin card the shape of each pattern piece (without the seam allowances) and put that between the felt and the lining; but for a hat designed to be worn by a human I would recommend buckram instead.

The main piece is drawn on a square of red felt.
Here's the main piece, prior to cutting out, with the card laid over it.
The pieces are now cut from the felt.  The card is not yet attached.
Both pattern pieces, with seam lines marked.
The side and top seams are both visible.  There is still no card.
The fez, inside out.

Because I used the narrowest seam allowance I could get away with (since felt doesn't fray, and in any case it was a very small hat), I didn't need to do any clipping to get the seam round the top of the hat to work. If you're using a wider seam allowance, you probably will. I think I didn't sew the whole of the side seam; I left the seam allowances at the top and bottom open, which would also have made it a bit easier.

It now looks pretty much like a fez.
The finished shell, right side out.
This image also shows glass-headed pins.  I had to use those because of the cats.
The lining pieces, cut from a darker red fabric, probably polyester or acetate.

Then it was just a question of cutting the same two pieces in the lining fabric and sewing them up in the same way...

The card surrounding the lining.  It seems to have been taped quite heavily to hold it together.
Sorry this is blurry. This is where the card finally got inserted.

...but the card was then a bit of a problem. I couldn't do the usual trick of sewing up most of the lower edge seam, turning it all the right way out through the hole, and then sewing up the rest invisibly from the right side, because that would have creased the card and rendered it useless for its purpose. (Honestly, I'd have used buckram for this one too, except that I didn't have any and wasn't going to buy any just for a demonstration fez for a penguin.) So what I had to do was pop the felt on top of this arrangement and then sew up the entire lower edge invisibly, or at any rate as invisibly as I could.

The lower edge being sewn up with tiny stitches.
Like this.

And, there you have it: Wilfred's very own fez, and the basic technique for making one any size you like. I'm happy to be able to tell you that I still have Wilfred; when I was taken into hospital in 2016, I knew they were going to admit me, so I packed a bag. I wasn't thinking very straight, since after all I was extremely unwell and it was the middle of the night, but Wilfred went into that bag, though I forgot several things that were probably technically more important. I didn't bring his fez, though.

I suppose I could make him another one; but he seems entirely happy without!

[Footnote: this originally went up on my SCA blog, which I think still exists, somewhere. However, I've written entirely new text for this entry, and I haven't quite used all the original photos, since one of them didn't seem to add anything useful. So if you find something similar to this anywhere else online, it's still me.]