Skip to main content

Klein Bottle Hat Pattern

Real Klein Bottle Hat

Read fun stuff about both Klein bottles and the origin of this pattern here:

Fits most heads, unless they are unusually large or small.


Worsted weight wool in your choice of colors. I used scrap wool that was given to me long ago. Lambs Pride worsted or Cascade 220 would work well. I used roughly 100 yards of each color. Maybe 150 for the main color (buff).

Set of US #8 DPN

Scrap yarn for provisional cast on
Yarn needle

I used a stripe pattern that I liked. I’m going to write the pattern as if the hat were all one color, but please put your own special pattern on it. This is a basic hat pattern with the addition of the weird tube at the top.


The “outside” of the hat will be knit first, then the “inside.” The “outside” part needs a hole to allow the tube from the “inside” to go through.


Cast on 80 stitches using provisional cast on.

Place marker and join in round

Work in [K1, P1] ribbing until the piece measures 5” from cast on edge.

Starting in the next round continue in ribbing pattern for 20 stitches, Bind off 4 stitches, continue in ribbing till marker. (76 stitches left on needles).

Work back and forth for 4 rows.

Work 20 stitches from marker, which should bring you to the bound off stitches.
Cast on 4 stitches using backwards loop cast on and work to marker. Continue in the round until the whole piece measures 6”

Begin decrease:

Work 10 stitches and place marker. Continue to end of round.

Work to first marker, knit two together, repeat to end of round.

Repeat this step till you have 16 stitches left on needles.

Knit in the round till the top tube measures 6”

Thread stitches through scrap yarn to hold them.


Pick up the 80 stitches from the provisional cast on.

Repeat as for inside till decrease except do not bind off stitches to create the hole.

The decrease will be done the same way, only instead of K2T you will P2T (yes, unorthodox, I know).

When you have 16 stitches left on the needles PURL till you have a 6” tube.

Hold stitches on scrap yarn.


Fold “inside” into “outside” pulling the tube of the inside through the hole in the outside. The knit side of the “inside” should now be seen.

Using kitchner stitch, graft the two tubes together. Lining them up will be difficult. The markers, which mark the start of the rounds should line up. This is tricky, but the only way to make it look like one continuous surface.

Wear to your favorite geek conference or present to your favorite math nerd.


  1. Knit the stripes as Pi, using black as the decimal point, and then just keep counting. Can be tricky keeping count of increases and decreases at the same time as Pi-ing the stripes, but you will have something unique!


Post a Comment

Popular Posts

How 4,000 Physicists Gave a Vegas Casino its Worst Week Ever

What happens when several thousand distinguished physicists, researchers, and students descend on the nation’s gambling capital for a conference? The answer is "a bad week for the casino"—but you'd never guess why.

Ask a Physicist: Phone Flash Sharpie Shock!

Lexie and Xavier, from Orlando, FL want to know: "What's going on in this video ? Our science teacher claims that the pain comes from a small electrical shock, but we believe that this is due to the absorption of light. Please help us resolve this dispute!"

The Science of Ice Cream: Part One

Even though it's been a warm couple of months already, it's officially summer. A delicious, science-filled way to beat the heat? Making homemade ice cream. (We've since updated this article to include the science behind vegan ice cream. To learn more about ice cream science, check out The Science of Ice Cream, Redux ) Image Credit: St0rmz via Flickr Over at Physics@Home there's an easy recipe for homemade ice cream. But what kind of milk should you use to make ice cream? And do you really need to chill the ice cream base before making it? Why do ice cream recipes always call for salt on ice?