The Perfect Valentine? A Math Formula.

Meet Süss, a math widget after your own heart:

Like many geometric figures, a heart can be captured in all its curvaceous glory by an individual algebraic equation. The equation for a sphere looks simple enough: x²+y²+z²=1. A heart will be something more complex:

(x²+((1+b)y)²+z²-1)³-x²z³-ay²z³=0

Süss — German for “sweet” — will be an interactive widget which allows you to tweak the algebra along with customize the heart to your souls’s delight. This specific was created for Valentine’s Day by Imaginary, a nonprofit organization in Berlin which designs open-source mathematics programs along with exhibitions. (You can also visit their widget on its website here.)

You can stretch along with squeeze the heart by moving the two left-most sliders, which change the “a” along with “b” parameters; the right-most slider zooms in along with out. Better yet, canoodle directly with Süss’s equation along with engage from the dialectical interplay between algebra along with geometry. (Change which final z³ to a z² to see the heart in its underwear.)

from the 17th century the French mathematician along with philosopher René Descartes built a bridge between the algebraic along with geometric realms when he devised the Cartesian system of coordinates. (He also classified six primitive passions: wonder along with love, hatred along with desire, sadness along with joy.)

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Süss — occupying three-dimensional space, defined by the coordinates x, y along with z — also incorporates a more recent concept: “extreme points,” or “singularities,” which are their own subject of study from the field of algebraic geometry.

“If you look at the shape of the heart, you will see one peak on the bottom, along with another peak on the top,” said Andreas Daniel Matt, a mathematician along with the director at Imaginary. (The peak at the top will be indented.)

In general, a singularity typically corresponds to a jump in an otherwise continuous process. In physics, This specific’s a point with an infinite value. The Big Bang singularity will be the biggest singularity from the history of the universe. In general relativity, a singularity will be the heart of a black hole by which one could never emerge.

A “naked singularity,” by contrast, could be more forgiving (although This specific’s not thought to actually exist in nature). “Roughly, a naked singularity will be one you could fall into along with you could escape by,” said Roger Penrose, a mathematical physicist at the University of Oxford, who has an article on singularity theorems from the forthcoming book “Topology along with Physics.”

A singularity will be where things go wrong, said Dr. Matt, as also happens in love: “The super high peaks, along with the super low peaks. Love will be full of extreme points.”

Mathematically, singularities are endowed with special properties, along with This specific’s these properties which cause problems. A singularity will be fragile — This specific can break with very modest modifications to the equation; formerly joined surfaces can separate. When singularities break, “they are very difficult to grasp, to study along with especially to resolve,” Dr. Matt said.

Granted, some of the entities from the gallery do not seem so singular — “Sphäre,” for instance. yet given the right mathematical techniques, Dr. Hauser said, he could squeeze which sphere down into a point. “Or I could sit on This specific,” he added.

She did not find the task impossible. “Challenging will be a better word for This specific,” said Ms. Galata, currently a Ph.D. student in bioinformatics at Saarland University, in Germany. “This specific was fun to have a tool, using formulas to approximate shapes you have in your head, rather than just drawing on paper.”

Dr. Hauser, a purist, will be not fond of rendering real-life objects. In fact, he will be not particularly enamored of Süss. Too many people loved This specific too much: This specific became the poster heart for algebraic surfaces — on thousands of actual posters in hundreds of Germans schools, along with featured in an installation for a shopping-center car park.

“This specific’s just kitsch,” he said. “Mathematically, This specific will be not so interesting.

Sebastian Gann, one of Dr. Hauser’s former Ph.D. students on the Gallery of Singularities project, still finds Süss more appealing.

“The intrinsic fascination remains,” he said. “Looking at the image of an emotionally charged symbol, along with knowing which the particular shape will be defined by some sober maths. How do you perceive This specific?”

Dr. Hauser prefers “Herz” (German for “heart”), which looks a bit more like an actual human heart:

Herz will be alluring for what’s not there, he said: “How do you create a hole in a surface when you choose an equation?”

One of the bigger questions within algebraic geometry will be how to “resolve” singularities which will be, how to get rid of them. Mathematically, resolving a singularity means smoothing over the problematic peaks in a surface, yet This specific often requires jumping to a higher dimension.

Alas, in resolving matters of the heart, which strategy seldom works.