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With SURFER you can experience the relation between formulas and forms, i. e. mathematics and art, in an interactive way. You can enter simple equations that produce beautiful images, which are surfaces in space. SURFER is the Java-based extension of the program SURFER2008 that was developed for the IMAGINARY exhibition in the year of Mathematics in Germany.
Mathematically, the program visualizes real algebraic geometry in real-time. The surfaces shown are given by the zero set of a polynomial equation in the variables x, y and z. All points in space that solve the equation are displayed and form the surface. As an example look at x2 y2 z2-1=0, the equation of a sphere. You can easily see that the point (x,y,z)=(0,0,0) is not on the sphere while the points (1,0,0), (0,1,0) and (0,0,-1) for example solve the equation. The program includes a big sample gallery with explanations and a tutorial. It is available in several languages including German, Spanish, Russian, Serbian and Portuguese.
The great thing about SURFER is that you don’t have to understand the underlying mathematics (algebraic geometry) a priori, you can experiment, try, follow your intution and creativity and this way learn maths and create unique art work like pictures or animations.