Towards a Reconstruction of Archimedes ' Stomachion

and Plan of Paper The Stomachion is the least understood of Archimedes' works. This paper provides a reconstruction of its goal and structure. The nature of the evidence, including new readings from the Archimedes Palimpsest, is discussed in detail. Based on this evidence, it is argued that the Stomachion was a treatise of geometrical combinatorics. This new interpretation is made possible thanks to recent studies showing the existence of sophisticated combinatorial research in antiquity. The key to the new interpretation, in this case, is the observation that Archimedes might have focussed not on the possibility of creating many different figures by different arrangements of the pieces but on the way in which the same overall figure is obtained by many different arrangements of the pieces. The plan of the paper is as follows. Section 1 introduces the Stomachion. Section 2 discusses the ancient testimonies and the Arabic fragment, while Section 3 translates and discusses the Gr~ek fragment. Section 4 sums up the mathematical reconstruction offered in this paper, while Section 5 points at the possible intellectual background to the work. Appendix A contains a transcription of the Greek fragment, appendix B an English translation with redrawn diagrams, appendix C a reproduction of the digitally enhanced images of the pages of the palimpsest containing remains of the Stomachion.