Talk:Surface (geometry): Difference between revisions

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imported>Catherine Woodgold
(Are surfaces necessarily infinite?)
imported>Greg Woodhouse
(Are surfaces necessarily infinite? - it depends)
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Is a surface only something like a plane or sphere, which has no edges, or would one face of a cube count as a surface?  If a surface necessarily has no edges, isn't it misleading to say it has length and breadth?  --[[User:Catherine Woodgold|Catherine Woodgold]] 20:20, 27 April 2007 (CDT)
Is a surface only something like a plane or sphere, which has no edges, or would one face of a cube count as a surface?  If a surface necessarily has no edges, isn't it misleading to say it has length and breadth?  --[[User:Catherine Woodgold|Catherine Woodgold]] 20:20, 27 April 2007 (CDT)
:I think the point here is that surfaces are 2-dimensional. In algebraic geometry, you can consider surfaces defined over arbitrartry fields (even finite ones), but in differfdential geometry you're pretty much limited to R (or C). But even in the case of algebraic surfaces, you usually work over an algebraically closed field and then talk about points definable (or "rational") over a subfield. [[User:Greg Woodhouse|Greg Woodhouse]] 21:37, 27 April 2007 (CDT)

Revision as of 21:37, 27 April 2007


Article Checklist for "Surface (geometry)"
Workgroup category or categories Mathematics Workgroup [Categories OK]
Article status Stub: no more than a few sentences
Underlinked article? Yes
Basic cleanup done? Yes
Checklist last edited by --AlekStos 14:46, 26 March 2007 (CDT)

To learn how to fill out this checklist, please see CZ:The Article Checklist.





Are surfaces necessarily infinite?

Is a surface only something like a plane or sphere, which has no edges, or would one face of a cube count as a surface? If a surface necessarily has no edges, isn't it misleading to say it has length and breadth? --Catherine Woodgold 20:20, 27 April 2007 (CDT)


I think the point here is that surfaces are 2-dimensional. In algebraic geometry, you can consider surfaces defined over arbitrartry fields (even finite ones), but in differfdential geometry you're pretty much limited to R (or C). But even in the case of algebraic surfaces, you usually work over an algebraically closed field and then talk about points definable (or "rational") over a subfield. Greg Woodhouse 21:37, 27 April 2007 (CDT)