The title page of Jost Buergi’s Progress-Tabulen (1620) is not only an eye catching masterpiece of the art of printing and a substrate of the tables inside, it also reveals fundamental insights into the nature of numbers and number systems.
The circular arrangement of the two number sequences links algebra with geometry by mapping the exponential function on an angular scale of red numbers to black numbers in the logarithmic place value system. In retrospect, the step from Buergi's diagram to the circular slide rule for multiplication seems a small one.
The lecture is intended as a contribution to the history of circular diagrams and volvelles – paper constructs with rotating parts – that emerged during the Renaissance. In particular, we will take a look at visualisations in contemporary music theory, which deal with closely related questions.
Opportunities to historically underpin and unconventionally motivate topics in mathematics education – geometric sequences, inverse functions, modulo arithmetic and number systems – emerge casually. Making calculating discs for music theory will sensitise learners for the fundaments of calculation techniques and number systems, and it promotes historically anchored, discovery-based learning. The transfer achievements to be made will sharpen the view for interdisciplinary topics.