1. ## Weird Graph

I once saw this graph which curled, intersected itself and then continued again.

Yes that's right, it CURLED

Does anyone know what the formula for a graph like that might be?

2. Originally Posted by janvdl
I once saw this graph which curled, intersected itself and then continued again.

Yes that's right, it CURLED

Does anyone know what the formula for a graph like that might be?
you mean something like this?

these are graphs in drawn with what we call POLAR COORDINATES, they are called Polar graphs i think

this particular one is given by:

$r = 1 + 2.5 \sin \theta$

(Note: if you graph this using the regular Cartesian coordinates, you will get a different graph)

3. Thanks Jhevon, but no, it had a normal f(x) formula.

I think it consisted of two formulas that were subtracted(or something!) from each other, but it was long ago and I cant really remember clearly.

And it only intersected itself once.

Like this:

4. The folium of descartes has a 'curl'. Is this it?.

It's equation is $x^{3}-xy+y^{3}=0$

One of my favorite is the 'butterfly'

5. Originally Posted by galactus
The folium of descartes has a 'curl'. Is this it?.
Thank you galactus, but no, sadly that wasn't it either. It looks like the one I drew. I remember exactly how it looked.

Wait, if we can invert that graph and maybe move it a bit forward and up, it will look like the one i drew.

That butterfly graph is absolutely amazing!!!

6. Galactus, draw up a polar graph using this formula:

e^(sin(t))-2sin(4t)+cos(t/4)^3

Your butterfly will now look as if it's flying.

-------------------------------------------

For an upright butterfly:

e^(sin(t))-2cos(4t)+cos(t/4)^3

--------------------------------------------

Here is a graph that looks as if it's radiating!!!

Polar graph of course.

e^(tan(t))-2tan(4t)+cos(t/4)^3

7. You had fun playing around with the butterfly.

Here's the equation which represents the 'pumpkin'. It's in spherical coordinates. See if you can graph it. You may have to convert to rectangular or polar. ${\rho}=a(1-cos({\phi}))$

8. the thing is that form of a graph coulden't posibly be a normal function. since all functions can't have two y relation ships for one x. that's what makes it a function of x. If I'm wrong about that then let me know.

other equations have relationships with y included. or it's posible that the equation is one that can be writen as two functions. or in this case three. Rather it is more likely to be a parametric or a polar graph.

But I do agree that playing with limacons are fun. try working with some archimedes spiral

r = n sin(theta)
when 0 < theta > 2pi*n and n > 1

they are fun to watch.

9. $r(t) = t sin(t)$

It looks like eyes tilted to the right.

10. sorry I'm mistaken I wrote the wrong equation

r = sin (t/n) | n>1

some use r = nt sin(t) 0<n<1 and I was trying to use that one but aparently I missed the t. Thanks for helping me corect it.