In this paper we are going to talk about Archimedes and the Stomachion with an aim to connect the main topic of our discussion with combinatorics, probability and number theory.
One need only cast a cursory glance at the well-known Archimedes “know-how”¯ with an aim to understand how this man was ahead of his time and in what could turn our world, if high technology would be assimilated in antiquity as fast as today. Archimedes majored in mathematics and geometry – the two most important sciences that underlie technological progress. Archimedes laid the foundations of integral calculus and the theory of numbers. He proved that the ratio of the circumference to its diameter is equal to the ratio of area of a circle to the square of its radius.
The revolutionary character of his researches was found in the fact that historians believe that Archimedes is one of the three greatest mathematicians of humanity.
Two thousand and two hundred years ago the great Greek mathematician Archimedes wrote a treatise titled “Stomachion”¯. Unlike other texts, written by Archimedes, the contents of this treatise, and even the meaning of the title was covered by darkness over the centuries. Some scientists consider that this treatise was devoted to combinatorics, the science that the ancient Greek scientists knew nothing in those days as it was previously thought.
The Stomachion was the less attractive treatise among all of Archimedes’ works, because its content was considered either insignificant or obscure. Over the past millennium remained only a tiny fragment of the introduction, and because the title seemed to be the same with the children gastric diseases, then this automatically invalidated the text of any interest in the eyes of many scientists. But times passed and the situation was greatly changed when scientists paid their attention on the children game the Stomachion. According to Netz and Noel, we see that “the game consisted of 14 flat ivory pieces of various polygonal shapes originally forming a square. The object of the game was to rearrange the pieces to form interesting things (people, animals, objects, etc.).”¯
This game took its origin in Archimedes’ treatise and the problem is solved only now on a very simple reason: for a long time mathematicians did not pay attention to it. Probably, the researchers did not discover its true meaning, and considered the Stomachion only the game for children, in which the 14 pieces allow children to create new shapes. The definition of the “elephant problem” was given to the Stomachion due to this erroneous interpretation.
According to different researches Archimedes was trying to establish how many cases of new configurations of the square can exist with its 14 constituent parts. The main goal of combinatorics is to determine in how many ways can be solved one or another task. Thus, it is a question of combinatorics, which has become an independent discipline only in the XIX century.
Taking into consideration the above stated information we could conclude that Archimedes was genius person who created the game Stomachion and only due to the fact that the meaning of the manuscript was incorrectly interpreted it was in shade for many centuries.
Netz, R. and Noel, W. The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist. Philadelphia, PA: Da Capo Press, 2009.