h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Which simple everyday word has the following precise definition in mathematics?

"An (n-1)-dimensional submanifold of an n-dimensional manifold, or in general, any codimension-1 subobject in an object"

Ask Fermat or Einstein. Assuming that the answer would make any kind of difference for the world.

I was going to say 'a pig in a poke?', but that's too many words, I guess.

I see what the maths is saying. I suggest either 'flattening' or 'projection'.

Me and my shadow
Strolling down the avenue

Not a projection - something more integral.

Cross section?

Not that either

Aspect? (That's what I'd call it)

No, it's an obvious part of the object in question - a simple word anyone would recognise

Diameter?

I know what it is

Is it easier to work out what it is by thinking about the 2 dimensional submanifold of a 3 dimensional manifold?

Not if you have no inkling what a "2 dimensional submanifold of a 3 dimensional manifold" is.

A 3d manifold is a more general version of a 3d space - a volume with length breadth and height. A 2d manifold is like a plane. So what's the everday word for taking a planar section from a 3d space?

Slice?

A planar or diametric section is just an arbitrary view of that space in that dimension. You need to define the whole.

Are we talking balloons here?

I think that's the best guess so far, Dmitri.

A picture or diagram?

Not a picture/diagram - that's just a projection of sorts.

There's something about the balloon which sums this up for simple objects.

Is it "sphere"?