# Four Math Sculptures

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## Crédits

- 3D-Data Modelling - Design and Construction

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This is the 3d-data for the 3d-printing of four small math sculptures, whose shape is described by precise mathematical formulas. All four represent classical mathematical curves or surfaces, namely the following: Barth Sextic, Dini Surface, Parabolic Cylinder and Plane (called Tülle), Rational Normal Curve. The data is in STL-format, and have a wall thickness of approximately 0.7mm, and a wire thickness of 3mm.

A 3D print of each of the four surfaces is part of the IMAGINARY Entdeckerbox.

The Barth Sextic is one of the so-called world record surfaces. It is a surface described by a polynomial of degree 6 in three variables. Among all those surfaces, it was the first examples with 65 so-called singularities (found around 1995 by W. Barth).

The Dini Surface is a surface with constant negative curvature which looks similar to a flower. The abstract mathematical surface extends infinitely, and has infinitely many “leaves”. We chose to show only two of those for this math sculpture.

Tülle consists of the union of two important shapes, a plane and a parabolic cylinder.

The Rational Normal Curve is the space curve parametrized by (t,t^{2},t^{3}). The object shows this space curve together with the three projections into the three coordinate planes. In the plane z=0, this projection consists of a parabola with parametrization (t,t^{2}). In y=0, it is a graph of a polynomial of degree three with parametrization (t,t^{3}). In x=0, the projection is curve with a cusp with parametrization (t^{2},t^{3}).

The math objects were designed by Herwig Hauser (Tülle) and Oliver Labs (the three others).

The 3d-data for all four mathematical objects were produced by Oliver Labs.

You can download the 3d-data to print the sculptures yourself for non-commercial use and while mentioning the author or you can order already printed sculptures online through our partner trinckle.com:

- Barth Sextik (Order 3d-print)
- Dini Surface (Order 3d-print)
- Tülle (Order 3d-print)
- Space Curve (Order 3d-print)