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:
$\displaystyle r = 1 + 2.5 \sin \theta$
(Note: if you graph this using the regular Cartesian coordinates, you will get a different graph)
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!!!
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
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.