# Talk:Half-space (geometry)

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Mathematics rating:
 Start Class
 Mid Importance
Field: Geometry

The picture with the red plane dividing R^3 into white space and blue space looks a bit wrong. Shouldn't the blue fill the entire half of the space above the red plane instead of just the one octant?--69.241.225.103 23:33, 22 September 2007 (UTC)

Would seem like that to me also. And I would note that in computer graphics, the words "half-space" are often used more generally, to describe any surface that partitions space into two distinct parts. (An infinitely long cylinder, or any closed shell, would all qualify as half-spaces.) 96.26.243.241 (talk) 07:40, 8 August 2008 (UTC)
it's definitely a mistake. Should be corrected. For now I corrected the title of the image. --205.155.65.233 (talk) 17:01, 8 April 2010 (UTC)

## Upper and lower half-spaces

Presuming that the terms "upper and lower half-space" are names for the regions on either side of the dividing plane, the definition given is only correct in the case when ${\displaystyle a_{n}=1}$ and ${\displaystyle a_{1}=...=a_{n-1}=b=0}$. The most general definitions would be ${\displaystyle a_{1}x_{1}+...+a_{n}x_{n}>b}$ for an upper half space, and ${\displaystyle a_{1}x_{1}+...+a_{n}x_{n} for a lower half space. These definitions don't say much more than the equations given at the top of the page, and could perhaps be incorporated into that section.

Also, no references are given in which these terms are used. Are they widely-used terms? — Preceding unsigned comment added by RawMoose (talkcontribs) 14:03, 19 December 2013 (UTC)