Το Οστομάχιον του Αρχιμήδη

CULTURAL PROGRAM: «Τhe Ostomachion of Archimedes: an ancient mathematical problem as well as an ancient puzzle» 

Secondary school of Rentina (prefecture of Thessaloniki, Greece) 

 In this program, the main goal was to gather information and study the following:

• The biography of the great Greek mathematician, inventor, physicist, engineer and astronomer, Archimedes
• The Palimpsest of Archimedes
• The Ostomachion of Archimedes
• Construct the Ostomachion of Archimedes and create our own figures

The Ostomachion (in Greek means the battle of the bones) of Archimedes is a square which consists of 14 geometrical pieces. It is beleived that, besides the fact that in ancient Greek was a game for children, Archimedes set also a mathematical problem, the first in combinatorics: how many different arrangements of the 14 geometrical pieces, that consists the ostomachion, are possible? The answer is 536 different distinct solutions! If we consider rotation, reflection and replacement of the same pieces (grey and blue, light blue and pink) there are 17.152 solutions. The mathematical problem was recently solved by a mathematician with a doctorate in mathematics from Cornell University, Bill Cutler. ( more info about the solutions of ostomachion in http://www.math.cornell.edu/~mec/GeometricDissections/1.2%20Archimedes%20Stomachion.html )