# More fun with Mathematica

## Play with the plots!

## A bumpy sphere

### Spherical plots can be used to model tumors

The spherical coordinate system

By plotting in spherical coordinates, mathematicians can easily model a variety of real world shapes. Here, our expression plots as a sphere of radius 1, give or take "c"^-1 according to our product of two sines term. Can you see how the term one forms the sphere and the sinusoidal term alters the shape? What shapes can you make?

Posted by Skip | 1/3/2014

## A toroidal spiral

### Is the structure of a tungsten filament in a lightbulb

This space curve is called a toroidal spiral.

Posted by Skip | 1/2/2014

## The twisted cubic

### A space curve with interesting projections

This curve is called the twisted cubic. Try rotating the viewing prism so you are looking at it dead on from different sides. What kind of line in 2 dimensions, or projection, does the space curve form?

Posted by Skip | 1/2/2014

## A quadratic surface

### Yet another 3D plot

Our next model examines the impact of a growing quadratic term in a fourth degree elliptic paraboloid.

Posted by Skip | 1/1/2014

## The Guassian Distribution...

### ...in two variables, of course!

Next we model a simple normal distribution in R^3. Within what radius, measured from center, would 68% of the volume fall? What about 95%? Hint: consider standard deviations.

Posted by Skip | 1/1/2014

## More Plots in R^3

### Visualizing another function of two variables using software

Here we model a damped oscillation, but this time damped with respect to one axis.

This one just looks cool:

Posted by Skip | 1/1/2014

## Plots in R^3

### Visualizing functions of two variables using software

Here we model a driven wave damping with radius to origin. One slider allows the windowing to be manipulated, while a second manipulates the exponent of the driving/damping envelope. Edit 1/1/14: Added more manipulation. H is the Height of the plot. R the range with respect to the X and Y axes. a is the exponent of the exponential. Observe how the wave radiates from origin!

Posted by Skip | 12/31/2013