The Unapologetic Mathematician

Mathematics for the interested outsider

Parallelepipeds and Volumes I

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November 2, 2009 - Posted by | Analytic Geometry, Geometry

5 Comments »

  1. […] and Volumes II Yesterday we established that the -dimensional volume of a parallelepiped with sides should be an […]

    Pingback by Parallelepipeds and Volumes II « The Unapologetic Mathematician | November 3, 2009 | Reply

  2. […] An Example of a Parallelogram Today I want to run through an example of how we use our new tools to read geometric information out of a parallelogram. […]

    Pingback by An Example of a Parallelogram « The Unapologetic Mathematician | November 5, 2009 | Reply

  3. […] Now that we’ve used exterior algebras to come to terms with parallelepipeds and their transformations, let’s come back to apply these ideas to the […]

    Pingback by The Jacobian « The Unapologetic Mathematician | November 11, 2009 | Reply

  4. […] to come back down again, covering the same region twice with opposite signs. This is related to the signed volumes we talked about, where (in one dimension) an interval can be traversed (integrated over) from left […]

    Pingback by Change of Variables in Multiple Integrals I « The Unapologetic Mathematician | January 5, 2010 | Reply

  5. […] because of this correspondence. In fact, it’s not hard to see that they’re related to signed volumes. This is the starting point from which all integration on manifolds emerges, and everything will […]

    Pingback by Integration on the Standard Cube « The Unapologetic Mathematician | August 2, 2011 | Reply


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