# Rotation in Flatland **URL:** \ **Category:** Factual Questions\ **Created:** [July 13, 2010, 1:06am UTC](https://boards.straightdope.com/t/rotation-in-flatland/546477 "2010-07-13T01:06:38Z")\ **Posts on this page:** 3\ **Page:** 2
**Author:** ![Cheshire\_Human](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Cheshire\_Human](https://boards.straightdope.com/u/Cheshire_Human)\ **Post date:** [July 15, 2010, 2:03am UTC](https://boards.straightdope.com/t/rotation-in-flatland/546477/21 "2010-07-15T02:03:25Z")
> [@Indistinguishable](#): > > Right, and even in 3d, there are numerous reasons why one would still want to refrain from identifying the codomain of the cross product with the domain of its two arguments (avoiding an arbitrary selection of unit magnitude and the pseudoproblem of pseudovectors/“handedness”). Life would be so much easier for students if we bothered to entrust them with abstract vector spaces (and the rest of abstract linear algebra) where useful instead of uglily pretending everything has to be done in R^n. **But old pedagogical habits apparently die hard.** [bolding mine] Yes, this was essentially my problem when learning about non-Euclidean geometries. My brother (1 year older than me, educated by the same people), when his son asked him for homework help on diameter / radius of circles, started to give him the standard “radius is half the diameter”. I took my brother aside, and said “yes, for Euclidean geometry, but that incredibly dumb **identity** between the two had to be **unlearned** by me before I could get non-Euclidean geometries [of which my brother was utterly ignorant]. Don’t load him down with that. Let me explain it.” My brother agreed (but only after I showed him examples of circles in non-Euclidean geometries that he never realized were non-Euclidean), so I explained radius vs diameter in a way that the kid will not be stuck on “radius = 1/2 diameter”. My elementary, and some high school, teachers were among the **biggest _impediments_** to my understanding of any concept beyond high school mathematics that I had ever encountered. ---
**Author:** ![chorpler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chorpler/32/2888_2.png) [@chorpler](https://boards.straightdope.com/u/chorpler)\ **Post date:** [July 15, 2010, 2:51am UTC](https://boards.straightdope.com/t/rotation-in-flatland/546477/22 "2010-07-15T02:51:29Z")
> [@Aspidistra](#): > > I thought you were going to ask a different question - how do they physiclaly do it? If I decide to spin in a circle I’m using the friction between me and the floor to give myself angular velocity, but of course in Flatland they don’t _have_ a floor, so what do they do? > > Um. That doesn’t seem to be the question you’re interested in though. NM, carry on… That’s why the Planiverse is a lot more interesting. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 15, 2010, 4:53am UTC](https://boards.straightdope.com/t/rotation-in-flatland/546477/23 "2010-07-15T04:53:44Z")
OK, **Chesire** , I’m not aware of any geometry in which the diameter of a circle is not twice its radius, and I can think of some pretty weird geometries. The closest I can come is in spherical Riemannian geometry with a radius more than a quarter of the circumference of the entire space, but I’d define such a circle as having the shorter radius, in which case we’re back to the diameter being twice the radius. Even if I use something crazy like the taxi metric or the video-game octagon metric, it still holds. Wait, I guess that in the discrete metric (where the distance between two points is 0 iff the points are identical, and 1 otherwise) all circles that exist have both circumference and diameter 1, but I’ve never heard anyone actually talking about circles in that metric (or indeed, using it for anything but trivial counterexamples), and I doubt that’s how you explained things to your nephew. [Previous page](https://boards.straightdope.com/t/rotation-in-flatland/546477.md?page=1)