1. ## Sketches in Maple

So, this is a unique project I was asked to do independently. I'm open to opinions and suggestions on it. Using parametric plots, polar plots, and other functions, I have to use Maple to create some type of drawing. It can be anything.

An example:

> with(plots):
> p1 := polarplot(5 + sin(3*theta), theta = 0..2*Pi, color = magenta, scaling = constrained):
> p2 := plot([2*cos(t), -1 + 2*sin(t), t = 5*Pi/4..7*Pi/4], color = red):
> p3 := plot([-2 + .8*cos(t), 2 + .6*sin(t), t = 0..2*Pi], color = blue):
> p4 := plot([2 + .8*cos(t), 2 + .6*sin(t), t = 8*Pi/7..13*Pi/7], color = blue):
> display(p1, p2, p3, p4);

By the finished product, I'm hoping to use around 50 different functions. Obviously I don't want to create some boring, easy-to-do drawing that only uses circles, lines, ellipses, and so forth.

Any suggestions?

2. Originally Posted by AfterShock
Any suggestions?
Create something for me.

I created a conjecture.
I did not try to prove it, but I want to see how it works in Matlab.

Conjecture: Let G(x) represent the Gamma function. Then if x1,x2,x3,...,xn are real numbers above 1 (including 1) we have that,

[G(x1+x2+...+xn)]^n <= G(n*x1)*G(n*x2)*...*G(n*xn)

Note: I have been able to prove if for n=2 (problem of the week).

I am hoping to first prove n=3 before attempting the generalized case. The good thing is that you can plot this in MatLab because it is a 3-dimensional graph. But you cannot above that. See if you can do that for n=3. Just be careful it does not overload the CPU!

One more note, equality only occurs when all are equal.