## Sylvester’s amphigenous surface

In the 19th century Sylvester described a surface for studying the number of real roots of a polynomial. Henrici later constructed a model of this. This is a modern version.

In the 19th century Sylvester described a surface for studying the number of real roots of a polynomial. Henrici later constructed a model of this. This is a modern version.

Oliver Labs
2017-03-27T09:54:29+00:00
all, discriminant surfaces, nonic surface (degree nine), strong and flexible|

This version of Clebsch's famous diagonal surface model features colored lines. One intersects the surfaces in a line and a hyperbola, the another one in three lines.

Oliver Labs
2017-03-27T09:15:45+00:00
Alfred Clebsch, all, Carl Rodenberg, Clebsch Diagonal Surface, for mathematicians, Ludwig Schläfli, multiple color sandstone|

A Togliatti quintic surface is a so-called world record surface. Among all quintic surfaces, it has the maximum possible number of singularities, namely 31. Our model is a smoothed version of such a surface.

The shape of our "four pillows meet pendant" is given by a single mathematical equation. Have you ever seen a pendant like this before?

Oliver Labs
2017-03-27T10:09:39+00:00
algebraic geometry, all, for art lovers, for mathematicians, for teachers, pendants, precious metal, precious plated metal|

Our "six pillows' secret pendant" is a very special piece of math jewelry. Its shape is given by a single equation. Have you ever seen a pendant like this before?

Oliver Labs
2017-03-27T10:06:20+00:00
algebraic geometry, all, for art lovers, for mathematicians, for teachers, pendants, precious metal, precious plated metal|

The photo shows a smoothed Kummer surface in steel (inflated with bronze). This post also features links to plastic versions of this shape. The Kummer surface is a classic from the 19th century; our model is a smoothed version of it.

This object looks like a piece of art. But in fact, it is "just" a mathematical curve, called 7/3 torus knot. Imagine a donut, and then tie a cord around it in some interesting way.

Oliver Labs
2017-03-27T09:58:19+00:00
all, curvature, exhibit "3d print studio" (2017-2018, at Cuyperhuis, Netherlands), for art lovers, for mathematicians, knots, speed curves series, strong and flexible|

Cubic surfaces are classics from the 19th century. This particular cubic is smooth and has tetrahedral symmetry. All 27 lines are real, but only 24 are visible in the model because 3 are infinitly far away.

This so-called Boy surface represents a fascinating example of a non-orientable surface. The first such surface was constructed by Werner Boy in his dissertation in 1902.

Oliver Labs
2017-02-16T13:21:05+00:00
all, for mathematicians, non-orientable surfaces, strong and flexible, Werner Boy|

In the 19th century, Olaus Henrici constructed a model of a quite symmetric cubic surface. This is a modern variant of it, allowing also to look "inside" of it from the bottom.

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