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
Arithmetic The Foundation of Mathematics three and ten and twenty comes from the Old English word twentizh which means two tens The numbers that are used for counting one two three four and so on make up a special class of numbers and are referred to as a class by several different terms They are called counting numbers whole numbers or positive integers from the Latin word integer meaning whole People use these numbers to count whole things such as one whole apple two whole days or three whole words They are also referred to as natural numbers because they were the first kinds of numbers that occurred to people and for a long time they were the only numbers that anyone used All the laws of arithmetic are based upon these counting or whole numbers When people learn to add subtract multiply divide raise to powers and extract roots they are learning to calculate with whole numbers Other kinds of numbers such as fractions negative integers and zero were not intro duced until much later when it was realized that new kinds of numbers were needed to make all the operations of arithmetic possible ARITHMETIC OPERATIONS Arithmetic evolved as a tool to help people 14
THE BEGINNINGS OF ARITHMETIC THE HISTORY OF MATHEMATICS People have used mathematics since ancient times The Egyptians could not have built the pyramids without a very good understanding of math especially arithmetic and geometry The Babylonians of ancient Mesopotamia now in Iraq invented a complex number system and used fractions The ancient Greeks greatly expanded math with many new ideas In about 300 BCE the Greek mathemati cian Euclid wrote an important book on geometry called Elements Later the Arabs also contributed greatly to math In the CE 800s an Arab mathematician named al Khwarizmi described a problem solving system that is now known as algebra The ancient Greek and Arab ideas about math even tually spread to Western Europe Math progressed as European scientists used it to research other subjects In the 1600s the astronomer Johannes Kepler used new mathematical ideas to study the skies Other scientists in the 1600s namely Galileo and Isaac Newton applied math to the study of motion In the 1800s and 1900s scholars developed many new ways to study and use math solve practical problems involving numbers or quantities Because they had to solve several dif ferent kinds of number problems people had to develop several different kinds of number operations In arithmetic the word operation refers to a method of combining two numbers 15
