# A Couple of Lingering Geometric Questions...
**URL:** https://boards.straightdope.com/t/a-couple-of-lingering-geometric-questions/818721
**Category:** Factual Questions
**Created:** [July 28, 2018, 8:15am UTC](https://boards.straightdope.com/t/a-couple-of-lingering-geometric-questions/818721 "2018-07-28T08:15:05Z")
**Posts on this page:** 2
**Page:** 3
### Author:  [@Andy\_L](https://boards.straightdope.com/u/Andy_L)
#### Post date: [August 3, 2018, 9:20pm UTC](https://boards.straightdope.com/t/a-couple-of-lingering-geometric-questions/818721/41 "2018-08-03T21:20:18Z")
> [@DPRK](#):
>
> That’s what I meant: start with 3-dimensional space, impose a single polynomial equation, and end up with a 2-dimensional subspace. (Over the real numbers it’s more complicated because of possibilities like x² + y² = 0, but we can stick with linear equations for the sake of this discussion.) Impose a second independent constraint and the dimension goes down to 1, etc. I just found **Isilder** ’s phrasing ambiguous so offered a concrete example (sphere, cylinder and plane work equally well to make this point).
Ah. Got it.
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### Author:  [@rat\_avatar](https://boards.straightdope.com/u/rat_avatar)
#### Post date: [August 3, 2018, 10:10pm UTC](https://boards.straightdope.com/t/a-couple-of-lingering-geometric-questions/818721/42 "2018-08-03T22:10:52Z")
> [@DPRK](#):
>
> That’s what I meant: start with 3-dimensional space, impose a single polynomial equation, and end up with a 2-dimensional subspace. (Over the real numbers it’s more complicated because of possibilities like x² + y² = 0, but we can stick with linear equations for the sake of this discussion.) Impose a second independent constraint and the dimension goes down to 1, etc. I just found **Isilder** ’s phrasing ambiguous so offered a concrete example (sphere, cylinder and plane work equally well to make this point).
It is a pity that complex and imaginary and real were the names given because they are far simpler in this domain but today’s XKCD is pretty funny.
> **[Complex Numbers](https://xkcd.com/2028/)**
>
> I'm trying to prove that mathematics forms a meta-abelian group, which would finally confirm my suspicions that algebraic geometry and geometric algebra are the same thing.
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