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Combinatorial Set Theory pp 177–190Cite as

How to Make Two Balls from One

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Abstract

For two reasons we shall give the reader a rest: one reason is that the reader deserves a pause to reflect on the axioms of ZFC; the other reason is that we would like to show Robinson ’s beautiful construction—relying on AC—of how to make two balls from one by dividing the ball into only five parts.

Rests, which are so convenient to the composer and singer, arose for two reasons: necessity and the desire for ornamentation. As for necessity, it would be impossible to sing an entire composition without pausing, for it would cause fatigue that might well prevent a singer from finishing. Rests were adopted also for the sake of ornament. With them parts could enter one after another in fugue or consequence, procedures that give a composition an artful and pleasing effect.

Gioseffo Zarlino

Le Istitutioni Harmoniche, 1558

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Authors and Affiliations

  1. Department of Mathematics, ETH Zurich, Zurich, Switzerland

    Lorenz J. Halbeisen

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  1. Lorenz J. Halbeisen
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Halbeisen, L.J. (2017). How to Make Two Balls from One. In: Combinatorial Set Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-60231-8_7

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