How to draw curves (cardioid, lemniscate, devil's curve)?

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Discussion Overview

The discussion revolves around the software options available for drawing complex curves, specifically the lemniscate, among others. Participants share their equations and seek recommendations for plotting tools.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant inquires about software to draw complicated curves, providing an equation for the lemniscate.
  • Another participant points out that the provided equation represents two straight lines, suggesting a misunderstanding of the equation's form.
  • Participants discuss various software options, including Gnuplot, Maple, Mathematica, Matlab, and GeoGebra, with some expressing a desire for more specific recommendations.
  • There is a correction regarding the equation format, with a participant acknowledging a mistake in their initial post.
  • One participant mentions trying out GeoGebra and seeks assistance with its Computer Algebra System (CAS) functionality.
  • Clarifications about the CAS feature in GeoGebra are provided, with suggestions on how to input equations for plotting.

Areas of Agreement / Disagreement

Participants generally agree on the availability of multiple software options for plotting curves, but there is some disagreement regarding the correctness of the initial equation provided and its interpretation.

Contextual Notes

Some participants express uncertainty about the specific capabilities of the software mentioned, particularly regarding the handling of implicit equations and the use of CAS.

Who May Find This Useful

This discussion may be useful for individuals interested in mathematical plotting, software tools for visualizing equations, and those seeking help with specific mathematical software functionalities.

ydonna1990
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Hi everyone,

Thanks for visiting my post. I was wondering if you guys know what kind of software I must use to draw complicated curves. I already have the equations. For example, for lemniscate I would use following:
2(x^2+y^2)=25(x^2-y^2)

I appreciate the help.
 
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mfb said:
There are many programs that can plot those curves.
Your specific example are two straight lines.
The example that I posted is Lemniscate's equation in Cartesian coordinates. Please refer to https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli
Anyway, I have the equations and I would like to draw the curves.

And as you said, I know that there are many software programs available. Can you provide me with a name.

Thanks.
 
Your formula is missing a square on the left side.

This list has many programs.
Gnuplot, Maple, Mathematica and Matlab are some of the more prominent plotting programs in this list.
ydonna1990 said:
I know that there are many software programs available
Then why did you ask which program you "must" use if there are so many options?

Edit: We don't delete threads, but I can close this one.
 
Last edited:
ydonna1990 said:
Can you provide me with a name.

Follow the link in post #2 and you will have one name. :smile:
 
The equation is 2(x^2+y^2)^2=25(x^2-y^2). I wrote my post in a hurry and didn't see the error until now.

Also as for the usage of the word "must", it could have easily been replaced with words like "could, should, may", etc. It's just a technicality. I apologize if you misunderstood.

Thanks for the list. It will come in handy.
 
jtbell said:
Follow the link in post #2 and you will have one name. :smile:

Well, one name, two names, three names.

Happy to be given a list eventually. I will def check out Gnuplot and Maple.
 
Check geogebra. It's free and it can handle these kind of implicit equations perfectly.
 
micromass said:
Check geogebra. It's free and it can handle these kind of implicit equations perfectly.
It's great. Thank you. I am trying it out now. I am trying to use CAS but it doesn't seem to plot. Any ideas?
 
  • #10
What's CAS? Is that part of geogebra, or does it mean you're using another Computer Algebra System?
If you're using geogebra, you just need to go all the way below to "input" and type your equation 2(x^2+y^2)^2=25(x^2-y^2). That should plot it immediately.
 
  • #11
micromass said:
What's CAS? Is that part of geogebra, or does it mean you're using another Computer Algebra System?
If you're using geogebra, you just need to go all the way below to "input" and type your equation 2(x^2+y^2)^2=25(x^2-y^2). That should plot it immediately.

CAS is part of geogebra. I just downloaded it and I am looking at it now. O.K. I will do that.
 
  • #12
Oh ok, I see it now. You don't need this CAS at all. It's better just to close that window.
 
  • #13
micromass said:
Oh ok, I see it now. You don't need this CAS at all. It's better just to close that window.
Alright. Do you think it'd be ok if I pm you some time later? (currently I am working on something). You are kind. I really appreciate your help.
 
  • #14
Sure, I don't mind.
 

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