Be my Valentine! Say it with Mathematics

Suppose you have an equation with three variables, such as x² + y² + z²-1 = 0. What does the set of all points (x, y, z) that satisfy this equation look like? In this case - Pythagoras sends its regards - it is a ball.

But understanding the solution of more complex polynomial equations is much more complicated. For example, what does (x² + ((1 + b) y) ² + z²-1) ³-x²z³-ay²z³ = 0 look like? You can test it yourself with the widget "Süss" (sweet) by IMAGINARY and Aaron Montag.

Raycaster for visualizing algebraic surfaces

To illustrate general algebraic surfaces, computer-aided tools are helpful. One class of such programs are raycaster. In this case, behind each pixel to be displayed, the intersection of the visual beam behind the pixel and the surface is approximated by a numerical method, and a harmonious color is calculated using the surface normals.

The raycaster "Süss" is really a by-product: Aaron Montag's dissertation deals with the development of the framework CindyGL, which simplifies graphics card supported implementations of mathematical algorithms. To test CindyGL and push it to the limit, the raycaster originally served as a benchmark. An algorithm for calculating zero written in mathematical high-level language is translated via Javascript into a WebGL-accelerated and therefore web-friendly application.

"I love you" as an algebraic equation

This Raycaster was discovered by IMAGINARY, a non-profit organization committed to teaching mathematics and designing open source math programs and exhibitions. That's how the interactive widget "Sweet" was created as a co-production of IMAGINARY and Aaron Montag based on CindyJS. Now you can use the above formula to visualize mathematical love greetings for Valentine's Day.

By moving the two left sliders, change the parameters 'a' and 'b' and stretch or squeeze the heart. The right slider zooms in and out.

And it gets even better: With "Süss" you can even adjust the equation and intervene in the dialectical interaction of algebra and geometry. Small tip: Change the last Z³ into a Z² and see the heart in panties.

Also The New York Times reports on the widget for Valentine's Day: The Perfect Valentine? A Math Formula