# Story that includes a description: “Two concentric circles, intersecting at three points” [duplicate]

I am trying to find a story I read as a child. I remember little about it except for the following:

• I suspect I read it before 1985, but it was a school library book which means it could be God knows how much older than that.

• This may mean it was a book meant for younger readers.

• In memory it "feels" longer than a short story, but I was a bit young to be reading novels. If I had to guess, I would guess novella length or shorter.

• English language, available in the United States.

• Contains several descriptions and ideas that stuck with me:

• The overall idea was that there were "parallel" worlds, parallel like the pages of a book, except for one that was (for whatever reason) skew to the rest, or warped somehow, and therefore intersecting the rest

• Geometry between that world and the rest seemed fundamentally incompatible as a result

• The most evocative example of this (by definition, since it is the only one I recall with clarity) is a description of... something... as looking like "Two concentric circles, intersecting in three places." This is obviously gibberish (concentric circles intersect nowhere unless they also have the same radius in which case they overlap perfectly; non-concentric circles that do intersect do so only at two points) but I was just old enough to realize it was gibberish being used to a purpose. It stuck with me.

• Technically speaking, in 3 dimensions you could have two concentric circles of equal radius, at 90 degrees to one another, which cross at two points. – Fifth_H0r5eman Aug 19 '19 at 11:05
• @Clockwork Non-Euclidean Geometry – popctrl Aug 19 '19 at 14:52
• Two concentric circles, intersecting at three points: this is possible if the two circles are identical in dimension, position, and, assuming 3D space, orientation. Of course, they actually intersect at ∞ points. If you're looking for circles that intersect at exactly three points, that's a different story.... – JakeRobb Aug 19 '19 at 18:04
• @Clockwork As popctrl said, you're probably thinking of Non-Euclidean Geometry, but that is not a branch of geometry where "everything is possible". Euclidean geometry states that if you have distinct lines A, B, and C such that neither A nor B intersect C, then A and B never intersect each other. (i.e. If A is parallel to C and B is parallel to C, then A is parallel to B). Non-Euclidean Geometries (e.g. elliptic or hyperbolic geometry) are any geometries that do not have that requirement. The rest of Euclid's axioms still apply. (On large scales, the universe may be non-Euclidean.) – Ray Aug 19 '19 at 22:01
• There's now a question on math.stackexchange about the specific geometry of this story. – Ray Aug 20 '19 at 9:53