Unformatted text preview: R 3 . We can think of the ordered triple ( A < B < C ) as deFning an oriented triangle, and hence associate to it a “signed” area. But which sign should it have—positive or negative? The question is illposed, since the words “clockwise” and “counterclockwise” have no natural meaning in space: even when A , B and C all lie in the xyplane, and have positive orientation in terms of the previous subsection, the motion from A to B to C will look counterclockwise only when viewed from above the plane; viewed from underneath , it will look clockwise . When the plane containing A , B and C is at some cockeyed angle, it is not at all clear which viewpoint is correct. We deal with this by turning the tables: 15 the motion, instead of being inherently “clockwise” or “counterclockwise”, determines which side of the 15 No pun intended! :)...
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 Fall '08
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 Calculus, Geometry, Vectors, Scalar, Vector Space, Pun

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