THE BEGINNINGS OF ARITHMETIC he term arithmetic comes from arithmos the Greek word for number People began doing arithmetic long before the Greeks invented the word however and even before anyone invented numbers ONE TO ONE CORRESPONDENCE Historians believe that as early as ten thou sand years ago when prehistoric people started farming they began to use arithme tic They needed to know such things as how many sheep they owned or how many rows of grain they planted or how long it would be before harvest season arrived According to historians prehistoric farmers devised an ingenious method for keeping track of things they used a process of matching that 10
THE BEGINNINGS OF ARITHMETIC AIG FRES Historians think that prehistoric shepherds figured out a smart system of matching that used pebbles or notches to keep track of every last sheep in their flock Photos com Thinkstock mathematicians call one to one correspon dence A shepherd for example could keep track of his flock by dropping a pebble into a pile or by cutting a notch in a twig for every sheep that went to pasture in the morning He could make sure that all his sheep returned home by matching them one by one to the pebbles in his pile or the notches on his twig This process of matching pebbles or notches with objects was the first step in the develop ment of arithmetic In fact two of the words 11
Arithmetic The Foundation of Mathematics that people use to describe doing arithmetic calculating and tallying come from the Latin words for pebble calculus and notch taleus One to one correspondence is still the most basic arithmetic process and it is so simple that even very young children use it Before they learn to count children can often put the right number of forks on the dinner table by laying out one for mama one for daddy one for brother one for sister and one for me COUNTING It is just a short step from one to one corre spondence to counting which is the process of matching objects with the names of numbers Counting is the second simplest arithmetic pro cess The earliest mathematicians thousands of years ago probably learned to count in much the same way as little children do today with their fingers When a young child wants to show how many people are in his family he or she might hold up a finger for each family member The child begins to count by reciting a specific num ber name for each consecutive finger he or she holds up one two three four It is not just coincidence that the Latin word for finger is digitus and that the ten numerals used in writing numbers o 1 2 3 4 5 6 7 8 and 9 are often called digits The names that people 12
THE BEGINNINGS OF ARITHMETIC It s no coincidence that number systems in modern languages such as English are based on the number ten which corresponds to our ten fingers iStockphoto com ausinasia invented for numbers came directly from count ing Most modern languages including English have base ten number systems that is they have separate number names only for the first ten numbers corresponding to the ten fingers used for counting Beyond ten the cycle of num ber names begins all over again For example in English the word eleven comes from the Old English word endleofan which means one left over Twelve is from the word trwelf meaning two left over Thirteen is clearly a version of 13
