Abstract
A cube cannot be transferred with ruler and compass into a cube of half the volume.
On the other hand, there are a number of easy-to-construct figures that
halve the cube volume. Symmetry considerations play an important role here.
With these figures, the space can be filled without gaps and without overlap.
We will discuss the difference between the static "fit in" and the dynamic
"fit into". We are working in the dimensions two, three and four.
For the production of the figures, among other things, the "monkey saddle" is used.
Similarly, we can work virtually with 3d origami.
Some examples are illustrated with paper models.
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Other talks of Hans Walser
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