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!

Multivariable Calculus Challenge Problem

  1. Dec 1, 2014 #1
    • Member warned about posting a problem with no effort
    1. The problem statement, all variables and given/known data
    Here it is:

    Let Ω be a convex region in R2 and let L be a line segment of length ι that connects points on the boundary of Ω. As we move one end of L around the boundary, the other end will also move about this boundary, and the midpoint of L will trace out a curve within Ω that bounds a (smaller) region Γ. Find an expression that relates the area of Γ to the area of Ω in terms of the length ι.

    2. Relevant equations
    See above.

    3. The attempt at a solution
    I have no idea. This is well beyond the scope of our course. The instructor put this out to get his students to reach out to the mathematics community and get involved in discussions of (multivariable) calculus. The closest I have come to encountering such a problem is related rates, but I have no idea how to do this.
     
    Last edited: Dec 1, 2014
  2. jcsd
  3. Dec 1, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    While you may not be able to do it in general (it seems really hard!) you might have some luck with special regions such as circular or elliptical disks, or maybe rectangles. Why not try the (seemingly) easier cases first? The concept of "envelope of lines or curves" seems to be relevant.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Multivariable Calculus Challenge Problem
Loading...