THE USES OF MATHEMATICS IN BABYLONIA to using 3 for m.However,another of their results giving the relation between the circumference of a regular hexagon and its circumscribed circle implies a value of 3 1/8 for A few volumes were computed,some correctly and some incorrectly,in the course of solving particular physical problems. Apart from a few special facts,such as the calculation of the radius of a circle circumscribing a known isosceles triangle,the substance of Babylonian geometry was a collection of rules for the areas of simple plane figures,in- cluding regular polygons,and the volumes of simple solids.The geometry was not studied in and for itself but always in connection with practical problems. 7.The Uses of Mathematics in Babylonia Despite the limited extent of the Babylonians'mathematics,it entered into many phases of their lives.Babylonia was in the path of trade routes and commerce was extensive.The Babylonians used their knowledge of arith- metic and simple algebra to express lengths and weights,to exchange money and merchandise,to compute simple and compound interest,to calculate taxes,and to apportion shares of a harvest to the farmer,church,and state The division of fields and inheritances led to algebraic problems.The majority of the cuneiform texts involving mathematics (exclusive of the tables and problem texts)were concerned with economic problems.There is no doubt as to the influence of economics on the development of arithmetic in the older period. Canals.dams.and other irrigation proiects required calculations.The use of bricks raised numerous numerical and geometrical problems.Volumes of granaries and buildings and the areas of fields had to be determined.The close relationship between Babylonian mathematics and practical problem is typified by the following:A canal whose cross-section was a trapezoid and whose dimensions were known was to be dug.The amount of digging one man could do in a day was known,as was the sum of the number of men employed and the days they worked.The problem was to calculate the number of men and the number of days of work. Because the connection between mathematics and astronomy became vital from Greek times on,we shall note what the Babylonians knew and did in astronomy.Nothing is known about Sumerian astronomy,and the as- tronomy of the Akkadian period was crude and qualitative;the development of mathematics preceded the development of any significant astronomy.In the Assyrian period(about 700 B.c.),astronomy did begin to include mathe- matical description of phenomena and a systematic compilation of observa- tional data.The use of mathematics increased in the last three centuries B.c. and was directed especially to the study of lunar and planetary motion.Most astronomical texts are from this Seleucid period.They fall into two groups