Question

Here is the "butterfly curve" traced out in Geogebra.

x(t) = sin(t) (e^cos(t) - 2 cos(4 t) - sin(t / 12)⁵)
y(t) = cos(t) (e^cos(t) - 2 cos(4 t) - sin(t / 12)⁵)

As the parameter t increases, a beautiful, symmetric, and ever changing non-periodic (because of the e^(stuff) terms) curve is traced out.

I've attached the geogebra file in the comments. I've also included a link to download geogebra (free graphing software which is awesome!) and another great free math tool for graphing 3d curves.

http://amath.colorado.edu/java/

http://www.geogebra.org/cms/en/installers

Answer 1

Here is the attachment.

Answer 2

thanks for the links

Answer 3

but can geogebra do\begin{array}l\color{#FF0000}{\text{R}}\color{#FF7F00}{\text{A}}\color{#FFFF00}{\text{I}}\color{#00FF00}{\text{N}}\color{#0000FF}{\text{B}}\color{#6600FF}{\text{O}}\color{#8B00FF}{\text{W}}\color{#FF0000}{\text{S}}\color{#FF7F00}{\text{?}}\end{array}

Answer 4

Yes it can! :) It supports different colors of graphs, fonts, etc.

Answer 5

I'll keep searching for free desktop software that helps me with Linear Algebra problems too.

Answer 6

whats important about a butterfly curve how does that help us in real life?

Answer 7

It's nothing. It's just a complex equation that yields an interesting graph.

Answer 8

>I'll keep searching for free desktop software that helps me with Linear Algebra problems too

Dr. Don Spickler's "Linear" software might be what you're looking for.
http://facultyfp.salisbury.edu/despickler/personal/Linear.asp

It's easy to use, and does a lot of cool stuff.

Though, honestly, wolfram alpha does just about everything you could ask with regards to linear algebra. : )

Answer 9

i graphed it on wolfram alpha and it looks like a butterfly how the hell does that happen?? is this magic?

Answer 10

>i graphed it on wolfram alpha and it looks like a butterfly how the hell does that happen?? is this magic?

It's a parametric equation. Basically, when you graph a normal function, you input a variable x, the function does something (multiply, divide, take sines, cosines, etc.) and spits out a number, y. You then take all the x values from, say -10 to +10, compute them and get a bunch of y values. You then plot all the points (x,y).

For a parametric function, each coordinate x and y is governed by its own equation! This allows circles, curves, and other such things which FAIL the vertical line test.

Much better description (with PICS) here: http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx

Use geogebra to graph it and see how the curve changes with time. :)