Re: Plotting a super ellipse

*To*: mathgroup at smc.vnet.net*Subject*: [mg55159] Re: Plotting a super ellipse*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Tue, 15 Mar 2005 00:21:41 -0500 (EST)*Organization*: University of Washington*References*: <d1148h$dqj$1@smc.vnet.net> <d13jam$qlp$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"JC" <Eat at joes.com> wrote in message news:d13jam$qlp$1 at smc.vnet.net... > On Sun, 13 Mar 2005 10:22:09 +0000 (UTC), Bob Hanlon <hanlonr at cox.net> > wrote: > >>Clear[x,y]; >> >>eqn=(x^(5/2)/1)+(y^(5/2)/(5/4)^(5/2))==20; >> <snip> >>Needs["Graphics`"]; >> >>ImplicitPlot[eqn,{x,0,xmax}, >> ImageSize->230]; >> >> >>Bob Hanlon >> > > Bob, > > Thank you very much for your response. It worked. Now I will just > need to decipher it so I can change the variables to adjust the > curve, but that is not a big problem. > > One question. The plot produced only was for one quarter of the super > ellipse. Is there a way to get the entire ellipse to plot? > JC, As written, your equation only has real solutions in the first quadrant. If you raise a negative number to the power 5/2 or 2.5, you surely cannot expect a real number. Perhaps your equation was supposed to include absolute values? Such as aeqn = Abs[x]^2.5 + Abs[y]^2.5/1.25^2.5 == 20; The above equation has roots in all 4 quadrants, and ought to be able to be plotted. Unfortunately, using ImplicitPlot with the above equation has problems, because ImplicitPlot calls Solve, and Solve converts Abs[x] into x || -x and then gives up. A workaround is to use Sqrt[x^2] instead of Abs[x]. So, let aeqn = Sqrt[x^2]^2.5 + Sqrt[y^2]^2.5/1.25^2.5 == 20; Now, if you use ImplicitPlot you will get a plot on all 4 quadrants. ImplicitPlot[aeqn,{x, -20^.4, 20^.4}] Carl Woll