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Research Station - Geometry & Dynamics

Contact

Secretary
Evelyne Bachmann

Mathematisches Institut
Universität Heidelberg
Im Neuenheimer Feld 205
69120 Heidelberg, Germany

E-mail
geodyn@mathi.uni-heidelberg.de

Further Outreach Projects

### Winter community projects (together with HEGL)

#### 2022/23: Let it snow! - Fractal Koch Snowflake

Replacing the middle third of a given length by the two segments of the same length that form an equilateral triangle with the replaced one, is one step of iteration to construct a Koch curve. The Koch curve is the limit of this iteration process. Three such curves together form a Koch snowflake, a nice fractal with a fractal dimension of about 1.262, which has infinite circumference but finite area.

This time we asked the community to build a fractal snowflake together. We distributed little Koch snowflakes and asked everyone to write or draw something related to math and/or winter on it. Thanks to many enthusiastic participants, we created a big snowflake out of 216 small ones and displayed it in the foyer of the Mathematikon. For more information and pictures, see the poster (in English and German), the explanations in English or German and the HEGL gallery.

#### 2021/22: Sierpinski Christmas Tree

The Sierpinksi triangle is a well-known fractal in two dimensions. Its pendant in three dimensions is the Sierpinski tetrahedron, where four small tetrahedra together form a bigger one. The fractal dimension of the Sierpinski tetrahedron is 2, which is the dimension of a plane, although the tetrahedron in a 3-dimensional object. Seen from the right perspective, the surfaces of the small tetrahedra form a plane without gaps and without overlappings.

We invited everyone to create one or more small tetrahedra and built a nice Sierpinski Christmas Tree out of them. For more information and pictures, see the poster and the HEGL gallery.

 Research Station Geometry & Dynamics - Contact: geodyn@mathi.uni-heidelberg.de.