Geometrikum - geometric exhibits to explore on the 3rd floor of Science Park 2

Hyperboloid of revolution - Hyperbolic plane - Klein bottle - Menger Sponge - Oloid - Sierpinski tetrahedron - Stanford bunny - Villarceau circles -- Various

wooden model of villarceau circles with shadow wooden model of Villarceau circles
Villarceau circles

In geometry, Villarceau circles are a pair of circles produced by cutting a torus obliquely through the center at a special angle (from Wikipedia).

Construction period: May 2016 - July 2016, more details here.

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Leopold the Lego Standford bunny
Stanford bunny

We built the Stanford bunny out of Lego pieces for the long night of science 2016.
Logo LNdF 2016

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Model of Hyperboloid of revolution made of wood and strings
Hyperboloid of revolution

A hyperboloid of revolution of one sheet. The strings are straight lines. For any point on the surface, there are two straight lines lying entirely on the surface which pass through the point. This illustrates the doubly ruled nature of this surface. From Wikipedia

Construction period: Feb. 2015 - March 2015, more details here.

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Menger Sponge fice versa made of paper, no glue was used. Menger Sponge made of paper, no glue was used.
Menger Sponge and vice versa, card cubes

In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension, see Wikipedia.

Instructions from the institute for figuring. Card cube instructions.

Construction period: May 2014 - July 2014. No glue was used! More details here.


Menger Sponge, perler beads
Menger Sponge made of perler beads

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Part of Sierpinski tetrahedron made of straws
A Sierpinski Tetrahedron made of straws

was built during the long night of science 2014.
Logo LNdF 2014

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model Hyperbolic plane crochet
Hyperbolic plane

2013, more information of the discoverer of hyperbolic crochet Daina Taimina on the homepage of the Crochet Coral Reef project.

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Grid of Klein bottle made of cable ties Floating Grid of Klein bottle made of cable ties and its shadow Model Klein bottle made of cable ties
Grid of Klein bottle made of cable ties


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Oloid made of wood and straws

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle. The distance between the circle centers equals the radius of the circles. One third of each circle's perimeter lies inside the convex hull, so the same shape may be also formed as the convex hull of the two remaining circular arcs each spanning an angle of 4π/3. From Wikipedia

Construction period: Autumn 2017.

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Match Circle Match cube showing Pi Match cube, only frame
Match Cube - Match Circle

2014, 2017, no glue was used!

Match Circle - they see me rolling

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Paper works

including a 12-unit stellated octahedron and a 30-unit stellated icosahedron made of Sonobe modules, furthermore, a truncated icosahedron.

No glue was used!

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Johannes Kepler Universität Linz, Institut für Angewandte Geometrie, Altenberger Str.69, 4040 Linz