"A difficult case": Pacioli and Cardano on the Chinese Rings

Abstract

The Chinese rings puzzle is one of those recreational mathematical problems known for several centuries in the West as well as in Asia. Its origin is difficult to ascertain but is most likely not Chinese. In this paper we provide an English translation, based on a mathematical analysis of the puzzle, of two sixteenth-century witness accounts. The first is by Luca Pacioli and was previously unpublished. The second is by Girolamo Cardano for which we provide an interpretation considerably different from existing translations. Finally, both treatments of the puzzle are compared, pointing out the presence of an implicit idea of non-numerical recursive algorithms.

A New Family of Number Sequences: Leonardo-Alwyn Numbers

“…Similarly, the characteristic equation of the Jacobsthal sequence is used in the Ernst sequence, and Jacobsthal's name is given to it. The Ernst sequence is also known as the Purkiss sequence (see, for example, [14], [15]).…”