Mathematics: The Study of Numbers, Quantity, and Space
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
Mathematics The Study of Numbers Quantity and Space Egyptian arithmetic based on counting in groups of 10 was relatively simple Base 10 systems the most widespread throughout the world probably arose for biological rear sons The fingers of both hands facilitated natural counting in groups of 10 Numbers are sometimes called digits from the Latin word for finger In the Egyptians base 10 arithmetic hieroglyphs stood for individual units and groups of tens hundreds and thour sands Higher powers of 10 made it possible to count numbers into the millions Unlike our familiar number system which is both decimal and positional 23 is not the same as 32 the Egyptians arithmetic was not posi tional but additive Unlike the Egyptians the Babylonians of ancient Mesopotamia developed flexible tech niques for dealing with fractions They also succeeded in developing a more sophisticated base 10 arithmetic that was positional and they kept mathematical records on clay tablets The most remarkable feature of Babylonian arithmetic was its use of a sexagesimal base 60 place valued system in addition to a deci mal system Thus the Babylonians counted in groups of 60 as well as 10 Babylonian 14
MATHEMATICS IN THE ANCIENT WORLD mathematics is still used to tell time an hour consists of 60 minutes and each minute is divided into 60 seconds and circles are mear sured in divisions of 360 legrees The Babylonians apparently adopted their base 60 number system for economic reasons Their principal units of weight and money were the mina consisting of 60 shekels and the talent consisting of 60 mina This sexag esimal arithmetic was used in commerce and astronomy Surviving tablets also show the Babylonians facility in computing compound interest squares and square roots Because their base 60 system was espe cially flexible for computation and handling fractions the Babylonians were particu larly strong in algebra and number theory Tablets survive giving solutions to first second and some third degree equations Despite rudimentary knowledge of geom etry the Babylonians knew many cases of the Pythagorean theorem for right triangles They also knew accurate area formulas for triangles and trapezoids Since they used a crude approximation of three for the value of pi they achieved only rough estimates for the areas of circles F 09 15
