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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'bivector'
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plane -> parallelogram ? by mps
Correction id: 12590
Filed on: 2007-06-23 10:00:50
Status: Accepted on 2007-06-23 11:12:34
Type: Meta/Minor
Correction text:
Shouldn't a bivector be viewed more as a directed parallelogram
(or ``unit of 2-dimensional volume'') than as the plane spanned
by the parallelogram? (After all, we separate the notions of
vector and line determined by the vector.) |
Comment from object owner PhysBrain:
>Shouldn't a bivector be viewed more as a directed parallelogram
>(or ``unit of 2-dimensional volume'') than as the plane spanned
>by the parallelogram? (After all, we separate the notions of
>vector and line determined by the vector.)
Actually, a parallelogram is a specific planar geometry element, when what we are interested in is just a generic plane-segment. The magnitude of the bivector can be used to represent the area of the specific planar geometry elements, be it a parallelogram, a triangle, a disc, or whatever. But as long as we are talking about a generic bivector in the same sense that we talk about a generic vector, then I think a plane-segment is the proper abstraction to use. |
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