Mathematics: The Study of Numbers, Quantity, and Space
MATHEMATICS IN THE ANCIENT WORLD athematics is often defined as the study l of quantity magnitude and relations of numbers or symbols It embraces the subjects of arithmetic geometry algebra calculus probability statistics and many other special areas of research There are two major divisions of mathe matics pure and applied Pure mathematics investigates the subject solely for its the oretical interest Applied mathematics develops tools and techniques for solving specific problems of business and engineer ing or for highly theoretical applications in the sciences 10
MATHEMATICS IN THE ANCIENT WORLD Mathematics is pervasive throughout modern life Baking a cake or building a house involves the use of numbers geom etry measures and space The design of precision instruments the development of new technologies and advanced computers all use more technical mathematics Mathematics first arose from the practical need to measure time and to count Thus the history of mathematics begins with the origins of numbers and recognition of the dimensions and properties of space and time The earli est evidence of primitive forms of counting occurs in notched bones and scored pieces of wood and stone Early uses of geometry are revealed in patterns found on ancient cave walls and pottery F 09 EGYPT AND MESOPOTAMIA As civilizations arose in Asia and the Near East the field of mathematics evolved Both sophisticated number systems and basic knowledge of arithmetic geometry and alge bra began to develop The earliest continuous records of math ematical activity that have survived in written 11
Mathematics The Study of Numbers Quantity and Space form are from the 2nd millennium BCE The Egyptian pyramids reveal evidence of a funda mental knowledge of surveying and geometry as early as 2900 BCE Written testimony of what the Egyptians knew however is known from documents drawn up about 1 000 years later Two of the best known sources for our current knowledge of ancient Egyptian The three pyramids at Giza line up within three sixtieths of a degree of true north south Space Imaging Europe Photo Researchers Inc Science Source 12
MATHEMATICS IN THE ANCIENT WORLD mathematics are the Rhind papyrus and the Moscow papyrus These present many differ ent kinds of practical mathematical problems including applications to surveying salary dis tributions calculations of the areas of simple geometric surfaces and volumes such as the truncated pyramid and simple solutions for first and second degree equations COMPARISON OF NUMERALS IN THE BASE TEN AND BASE Two SYSTEMS NUMERALS Base TenBase Two Base Two Owe Owo 1Orwe 10 11 two 1 1000 1 0 4 100rwo Any Ph An LTR HRT I F 09 Pan An Amarass in A Dylan Th TD 0 0 0 0 111two 1 2 8 1000we 2 x 2 1000 we 16 10000two 1 2 x 2 x 2 x 2 0 0 0 0 16 100000 19 10011 TR 2 x x 2R 2 FO T T e X 16 0 0 2 1 10011two The simplicity of the binary system makes it ideal for use in computing Encyclopaedia Britannica Inc 13
