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: How to plot this region in (x,y) space

  1. Nov 19, 2005 #1
    Hi everyone

    I need some help with an elementary problem...I have to sketch the region described by

    [tex]max(|x|,|y|) \leq 1[/itex]

    I know what max and mod (absolute value) mean but I'm just troubled because of the occurence of [itex]|y|[/itex]. Any help would be appreciated...

    PS--This is not homework.

    Thanks and cheers
  2. jcsd
  3. Nov 19, 2005 #2
    This is just the desciption of the square of 2unit side length, centered in (0,0). Usually in that kind of formalism, (x,y) are describing the coordinates of a point on a "ideally" flat infinite plane...In your case you just take all points for which -1<=x,y<=1 which is separated into -1<=x<=1 and -1<=y<=1, because there is no relationships between x and y given here.
  4. Nov 21, 2005 #3

    The thing is..how do you reconcile with the occurence of [itex]|y|[/itex]?? I mean....how are you to compare the two operands? Are x and y independent variables in the two orthogonal directions?

    I know that

    [tex]max(x,y) = \frac{x+y}{2} + |\frac{x-y}{2}|[/tex]

    Does this fit in somewhere?
  5. Nov 22, 2005 #4
    Yes, x and y are independent...you just compare as the max functions say : max(x,y)=x if x>y and max(x,y)=y if y>x....you could do : max(|x|,|y|)<=1 equiv. to |max(x,y)|<=1 and with your formula : [tex] \frac{1}{2}|x+y+|x-y||<=1[/tex]
  6. Nov 26, 2005 #5
    I'm sorry I'm somewhat dumb...I can't see how I can plot the max of two independently varying numbers...some more spoonfeeding needed. :biggrin:
  7. Nov 26, 2005 #6


    User Avatar
    Science Advisor

    If |x|< |y| then max(|x|,|y|)= |y|. Graph |y|= 1.
    If |y|< |x| then max(|x|,|y|)= |x|. Graph |x|= 1.

    Those two graphs form the boundary of the region. Now do you see what the region is?
  8. Nov 28, 2005 #7
    Great. Thanks! I see it now :smile:

    I realize how dumb I've been throughout this thread!!!! :cry:

    Anyway thanks for all your help.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook