One of the answers in my crossword today was KLEIN BOTTLE which set me wondering where Felix first described his famous mathematical object. It turns out the answer is (as far as we can tell) a set his handwritten lecture notes 1882 and after some searching I was able to find a facsimile of the relevant page at kleinbottle.com.
But along the way I found that Klein never called it a bottle. He called it a Fläche, 'surface', related to English ply and pleat, but it got misread as Fläsche, 'bottle' related to English flask and flagon.
Why? The obvious answer is they couldn't read his handwriting, but I'm not convinced. The word Fläche appears four times on the relevant page and is written in quite a clear and consistent way.
So maybe someone simply thought 'bottle' worked better than 'surface' (it does) or maybe it was a flash of inspired humour. Who can tell? But below I have pasted an image of the page (courtesy of kleinbottle.com.)
With a steer from Copilot I was able pick out and highlight Fläche in four places and you can judge for yourself whether it is legible. And as a bonus you get to see Klein's sketches where he is showing that if you just join the end of a cylinder in the obvious way you get an anchor-ring (or torus), but if you join them so the end have opposite orientation you get a one-sided surface.
