[IndigoSpinner]

This is a genuine question, not a snarky remark. I never understand when people say it's not a moebius to knit flat and twist and seam it together. If you make a moebius strip from paper, that's exactly what you do. Why not in knitting?

It'a not a snarky remark. If you have a cowl and want to call it a smoke ring or an endless scarf, or a number of other names, that's fine. They all work.

But a mobius is a mathematical construct. It doesn't have a lot of different names, and it's description is mathematically precise. It has one surface, and one edge.

I think what people mean when they erroneously say that is that you can't cast on in the round and twist it and produce a mobius. The reason is that when you do that, it introduces a full twist (360 degrees) rather than the half-twist (180 degrees) that is needed for a mobius. But people who don't understand the construction misunderstood them because they didn't fully qualify what they were saying.

But, if you knit lengthwise, as if you were making a scarf, and then join the ends with a half twist, that's a mobus. It fits the definition.

 

[IndigoSpinner]

A recent issue of Knitter's Magazine had an article with (I think), three ways to cast on for a mobius.

No, the cover says 4 cast-ons! https://www.knittinguniverse.com/K118/

 

[IndigoSpinner]

When one uses a Mobius cast on and knits, you are knitting two side at once. The cast on is really in the center of the work that is why you see both stockinet and garter stitch as you knit. You are knitting in two different directions at the same time.

If you only do knit stitches, you see stockinet and reverse stockinet.

You are actually only casting on on one side even though you're knitting stitches on the first round from first one side of the needle and then the other.

A true mobius has only one side and one edge. You cast on in the middle and work out.