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blueshift
2005-Sep-10, 11:40 PM
I have been reading and rereading John Archibald Wheeler's "A Journey into Gravity and Spacetime".
Many of the concepts take a while for beginners and still take a while for slower learners like myself..I am curious about something. Am I right or wrong about the following?

Wheeler seems to make some emphasis on "embedding" and at times I can't figure out why...until I got to thinking of how I would draw a cube on a piece of paper. I would have to draw a square with two other parallelograms that each shared an edge with one another and where each shared an edge with the square..

However, the angles of those parallelograms would not be 90 degrees as far as my drawing them is concerned but still have to represent 90 degrees..Their edge lengths will not be equal to the square's (except where they share the edge with the square) but must represent an equality or there is no cube..

Therefore, I assume that the math to describe this situation accurately has to deal with slight deviations in angles and lengths...Is this one of the origins of thought behind the need for tensor calculus?

jkmccrann
2005-Dec-12, 07:39 PM
Maybe this should be in the Q & A section, because it is an interesting question that I unfortunately don't have the answer too.

hhEb09'1
2005-Dec-20, 08:18 PM
Their edge lengths will not be equal to the square's (except where they share the edge with the square) but must represent an equality or there is no cube..Actually, some engineering drawings would represent just such a cube, where all edge lengths are equal. Angles would be 60 degrees (or 120).