Egyptian Counting with Hieroglyphs-gctid29266

[Kala Kambon]

   
 
EYPTIAN COUNTING WITH HEIROGLYPHS

These are the basic glyphs (symbols) used       in Egypt for counting over 4000 years ago:                     =1                 =10                 =102=100                 =103                 =104             =10000                 =105                 =106                 =107            Writing an integer consists of writing the       number (from 0 to 9) of the proper symbols to represent the integer.       Thus,         3105 = 3*(1000)+100+5 = .            There is also a glyphwhich       can translated as "equals" and a compact way of writing       large glyphs, as shown below on the right, for two ways 35:         .

       
 
Addition & Subtraction
in early Egypt

Addition and subtraction were simple processes       using the counting glyphs. To add       two numbers, collect all symbols of similar type and replace       a ten of one type by one of the next higher order. For example,       adding 35 and 17:                                           add                                                Subtraction is a       reversal of the process, if necessary replace a higher, so                                 subtract

     
 
Multiplication and Division

Multiplication and Division       were also simple processes using the counting       glyphs. To multiply two numbers, all you needed to understand       was the double or the half of an integer; i.e., the 2 times       table. For example, to multiply 35       by 11. You successively multiply double 35 (and its doubles)       at the same time as doing this to 1, until just before you get       to 11 in the latter. Below we first do this in present day notation,       and then give the translation into glyphs the way the ancients       would have done.                     1*                 35                 2*                 70                 4                 140                 8*                 280                 1+2+8=11                 35+70+280=385                Division, up to fractions,       is just a reversal of the multiplication process, where it seems       the egyptian did not think of, say "divide 1075 by 25."       Instead the question was posed as "how many times should25       be added to itself to yield 1075." Specifically, to divide       1075 by 25, again double,1 on the left , 25 on the right until       just before you surpass 1075. Unless we have no whole number       divisor, some choice of sums on the right equals 1075. Choose       the corresponding rows on the left                     1                 25*                 2                 50*                 4                 100                 8                 200*                 16                 400*                 32                 800*                 1+2+8+32=43                 25+50+200+800=1075                What happened when one divided 1079 by 25?       We would write 43+4/25. However, the Egyptians did not write       the fraction 4/25. Instead, you might see 1/10 + 1/20 + 1/100       or 1/8 + 1/40 + 1/100 (see       egyptian fractions).

     
Egyptian Arithmetic - Mathematicians of the Kmtyw Diaspora





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