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KaBoL is a "cool math site of the week" service to the mathematics
community offered by the Canadian Mathematical Society. It is
available at http://www.camel.math.ca/Kabol/ .

If you've worked with graphic softwares like Freehand, you should be familar with the Bezier Curve. 

According to WiKipedia, In the mathematical field of numerical analysis, a Bézier curve is a parametric curve important in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

I used GD graphic library and eval() fucntion is PHP to develop the Bezier class. This class takes the coordinates of 4 points needed for a bezier curve and draws it in an image. This image can be saved like any other web image. You can draw your own Curve by clicking on the following sample image.

The class code can be downloaded from my page in phpclasses.org.

Try it here! 

According to Wikipedia, A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"^[1] a property called self-similarity.  

Recently I added a post about a Silverlight application to draw Koch Curves. I re-programmed it in PHP using the PHP GD image library. The output is a Jpeg and can be saved like a normal image. You can try the application by clicking on the sample image. The only input you need to provide is the number of iterations (levels) which can be selected from the given dropdown.

You can also download the PHP code from phpclasses.org. Click on the sample image to try it yourself.

As a Flash and C# developer, I was always curious to try SilverLight so I read a book on SilverLight 2.0 and really enjoyed it. I tested my SilverLight knowledge by doing a "cool" application on fractals.

According to Wikipedia, A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"^[1] a property called self-similarity.

You can try it here. In the first textbox, you need to enter the number of recursion levels. I don't recommand anything over 7. In the second textbox, you need to enter the size of the recursion in pixels. After setting these values, press the button.

IE should be used to try this demo and SilverLight 2.0 plugin must be installed.

This cool PHP script takes an expression, f(x) and calculates all the roots between a start and end point. It also provides a nice graphical output which can be saved.

Here is  a sample output:

You can try it yourself here. The code is downloadable from phpclasses.org.

This class takes x(t) and y(t) as a parametric equation and draws its diagram in jpeg format.

Here is a sample output:

Try it yourself. You can download the code here.

Remember old high school days?

the integral

is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b.

This cool PHP script, gets a diagram expression, start and end point for the variable x and calculates the integral of the given expression between start and end points. You'll also get a nice diagram with a graphical representation. You can increase the accuracy of the caclulation by choosing a smaller calculation step from the dropdown menu. Obviously the smaller the step is, the longer the calculation be.

Here is a sample output for f(x)=sqrt(x)*5

Try it here. The code is also downloadable from phpclasses.org.

When I was a student at universoty, I used to do lots of scientific PHP programs just for fun. Here is the one I really like. After 7 years I still can spend time playing with it and graw really cool graphs.

This PHP application takes 3 parametric expressions for x, y and z dimentions and draws the 3D graph representing the expressions. You can also save the result as an ordinary image. This program is really useful for students who like mathematics and algebra. 

t, is the variable which changes within the range you provide so foreach specific t, we will get a x, y and z values which will form our cool 3D graph

Here is a sample output:

You can try it here. Just make sure you type the expressions in C++ (PHP) format. This code can be downloaded here.