1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector Calculus Problem

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data
    Let R be the unit square such that R= [0,1] x [0,1]
    Find a sequence of partitions of R such that the limit as k ->inf of the area of the largest sub-rectangle of the partition (where k is number of partitions) goes to zero but the mesh size does not go to zero.
    Depicting the first couple of partitions in the sequence graphically suffices.

    2. Relevant equations

    3. The attempt at a solution
    I know how to show the converse, i.e. showing that if the mesh size goes to zero, then the area of the largest sub rectangle goes to zero. In this case, the mesh size is the Euclidean norm of the i'th sub-rectangle: if I divide the square into 4 unequal sub-rectangles, then: 0 < 4(maxA(R)) < 4mesh^2 (i.e. Euclidean Norm squared) so by taking the limit of the mesh, and if it tends to zero, then the max area will tend to zero by squeeze. I'm having trouble starting the aforementioned problem, though.
  2. jcsd
  3. Jan 25, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Think about long skinny rectangles.
  4. Jan 25, 2015 #3
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted