Matt Parker (aka StandupMaths) says:

“The Klein Bottle is a topological surface discovered by Mr Klein in 1882. It’s a twisted torus (donut) in the same way that a Möbius Strip is a twisted loop… .

“Klein Bottles have been knitted before (see fantastic examples by Marie-Christine Mahe on knitty.com) but I wanted to raise the mathematical stakes. So I worked with my poor Mum to make a stripy Klein Bottle hat, where each stripe represents a different digit of Pi.

“Please email me any photos of you wearing this hat. If there exists a more nerdy hat anywhere, please do let me know.”