# [Maxima] cardioid

Mario Rodriguez biomates at telefonica.net
Sun Mar 30 13:02:55 CDT 2008

```Adam Majewski escribió:

> So the problem is he name of argument ?
> I have changed "t" to "theta" :
>

No, you can use the name you want, but you have to transform t to
something else, let's call it theta, which should be a true argument;
that is, the angle formed by the x-axis and the radius, or in other
words, the angle such that x=r*cos(theta) and y=r*sin(theta).

In my previous post, the Maxima code shows that the point associated to
%pi/2 doesn't rest on the y-axis.

> (%i1) e1:exp(theta*%i)/2-exp(2*theta*%i)/4;
> (%o1) %e^(%i*theta)/2-%e^(2*%i*theta)/4
> (%i2) r:abs(e1);
> (%o2)sqrt((sin(theta)/2-sin(2*theta)/4)^2+(cos(theta)/2-cos(2*theta)/4)^2)
> (%i4) draw2d(nticks = 2000, xrange = [-2.5,0.5], yrange=[-1.5,1.5],
> color = blue, line_width= 3, polar(r,theta,0,2*%pi),grid=true)\$
>
> but it gives the same curve.
>

Of course. You have only renamed the parameter, but this is not the key
question.

>
>> If you want to draw a cardioid in polar form, use equation
>> r=k*(1-cos(theta)):
>>
>> (%i8) draw2d(polar(5*(1-cos(theta)), theta,0,2*%pi))\$
>
> It works good but this is diffrent cardioid.
>

Sure, I chose coefficient 5 at random. My intention was to show how to
draw a cardioid in polar form, but I haven't looked at the
transformation to be performed.

--
Mario Rodriguez Riotorto
http://www.telefonica.net/web2/biomates
```