# Weird Graph

• Jul 4th 2007, 11:52 AM
janvdl
Weird Graph
I once saw this graph which curled, intersected itself and then continued again.

Yes that's right, it CURLED :eek:

Does anyone know what the formula for a graph like that might be?
• Jul 4th 2007, 11:58 AM
Jhevon
Quote:

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

Yes that's right, it CURLED :eek:

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)
• Jul 4th 2007, 12:06 PM
janvdl
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:
• Jul 4th 2007, 12:18 PM
galactus
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'
• Jul 4th 2007, 12:20 PM
janvdl
Quote:

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!!!
• Jul 4th 2007, 12:44 PM
janvdl
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!!! :D

Polar graph of course.

e^(tan(t))-2tan(4t)+cos(t/4)^3
• Jul 4th 2007, 01:24 PM
galactus
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. ${\rho}=a(1-cos({\phi}))$
• Jul 6th 2007, 09:28 PM
servantes135
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.
• Jul 7th 2007, 01:28 AM
janvdl
$r(t) = t sin(t)$

It looks like eyes tilted to the right. :D
• Jul 7th 2007, 02:13 AM
servantes135
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.

:)