An IMAGINARY exhibition is staged at the Explore Science fair of the Klaus Tschira Stiftung in collaboration with the Mathematisches Forschungsinstitut Oberwolfach in the Luisenpark, Mannheim.

# SURFER

program

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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.

## Featured User Gallery

Valentina Galata, now student of bioinformatics in Germany, started to use the surfer as a high school student in 2008. She specialized in remodelling real world objects with SURFER. She found equations that create images of fruits, design objects or landscapes. Generally she adds several surfaces to one image by multiplying their equations, often variations of basic geometric figures, like spheres or cones.

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 x^{2}+y^{2}+z^{2}-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.

SURFER is the new, Java-based version of the program SURFER2008 that was developed for the IMAGINARY exhibition in the year of Mathematics 2008 in Germany. The program is platform-independent and runs on a Windows, Linux or Mac operating system. SURFER has been used for many IMAGINARY exhibitions and is constantly improved and extended.