This history of the calculator gioes backj a long way. The decimal numbering system is based on the number ten because the earliest calculating devices were the ten fingers found on the human body. As human intelligence developed, calculators evolved to incorporate pebbles and sticks. In fact, the word calculator comes from a form of the late fourteenth century word calculus, which originally referred to stones used for counting. Long before the inception of the word, many different ancient civilizations used piles of stones (as well as twigs and other small plentiful things) to count and perform basic addition. However, counting out large piles of stones had limitations (imagine counting 343 stones and then adding 421 stones to find the sum). As civilizations progressed, needs for more efficient calculators increased. For example, more and more merchants were selling their goods in the growing towns, and keeping track of sales transactions became a common need.

Around 300 B.C., the Babylonians used the first counting board, called the Salamis Tablet, which consisted of a marble tablet with parallel lines carved into it. Stones were set on each line to indicate how many of each multiple of five were needed to represent the number. Counting boards similar to the Salamis Tablet eventually appeared in the outdoor markets of many different civilizations. These counting boards were usually made of large slabs of stone and intended to remain stationary, but people with more money could afford more portable boards made of wood.

The abacus took the counting board methods to another level by allowing beads to be slid up and down small rods held together by a frame. The word abacus stems from the Greek word abax, meaning table, which was a common name for the counting boards that became obsolete with the popularization of the abacus. Historians believe that the first abacus was invented by the Aztecs between A.D. 900 and 1000. The Chinese version of the abacus, which is still the calculator of choice in many parts of Asia, first appeared around A.D. 1200. In A.D. 1600, a Russian form of abacus was invented. A Japanese style of Abacus was invented in 1930 and is still widely used in that country. The rods of most abaci are divided into two sections (called decks) by a bar, with the

beads above the bar representing multiples of five. A top bead in the ones column represents five, a top bead in the tens column represents 50, and so on. Some abaci have more than two decks. In 1958, the Lee abacus was invented by Lee-Kai-chen. This abacus is still used in some areas. It can be thought of as two abaci (the plural of abacus) stacked on top of each other, and is supposed

to facilitate multiplication, division, and other more complicated operations.

Mathematical tables and slide rules were two of the most common computational aids before small electronic calculators became reasonably affordable in the 1970s. Mathematical tables were used for thousands of years as a convenient way to find values of certain types of mathematical problems. For example, finding the value of 23 multiplied by 78 on a multiplication table only requires finding the row next to the number 23 and then following that row until reaching the column labeled 78; no computation is necessary, and finding the value takes little time.

The first slide rule was created in 1622. A typical slide rule consists of a two or more rulers marked with numeric scales. At least one of the rulers slides so that two or more of the scales move along each other. Different types of slide rules can be used to reduce various complex operations to simple addition and subtraction. By aligning the scales in the proper positions and observing the

positions of other marks on the rulers, a trained user can make quick computations by reducing multiplication and more complex operations to simple addition. Slide rules, along with mathematical tables, remained two of the most useful mathematical tools until they were made obsolete in most areas of computation by the invention of electronic calculators.

The invention of the slide rule was dependent on the discovery of logarithms about a decade earlier because the scales on a slide rule involve logarithms. John Napier was the first to publish writings describing the concept of logarithms, though historians also point out that the idea was most likely conceived a few years earlier by Joost Bürgi, a Swiss clockmaker. The math behind the discovery and development of logarithms is beyond the scope of this text, but their main contribution to science and mathematics lies in their ability to reduce multiplication to addition, division to subtraction. Furthermore, exponents can be found using only multiplication; and finding roots only involves division. For example, when using a table of logarithmic values to multiply two large

numbers, one only needs to find the logarithmic values for both of the numbers and add them together. The invention of the slide rule made it possible to work with logarithms without searching through large tables for values.

Many mechanical calculators were invented before the electronic technology used in modern calculators came about. One such mechanical calculator, the Pascaline, was invented in 1642 by 19-year-old French mathematician Blaise Pascal. The Pascaline was based on a gear with only one tooth attached to another gear that had ten teeth. Every time the gear with one tooth completed a turn it would cause the other gear to move a tenth of the way around, so the gear with ten teeth completed one turn for every ten turns of the gear with one tooth. Using multiple gears in this way, the Pascaline mechanically counted in way similar to a person counting on their fingers or using an abacus. The concepts first explored in the Pascaline mechanical calculator are still used in things like the odometer that keeps track of how far an automobile has gone, and the water meter that keeps track of how much water is used in a household.

Compact electronic calculators were made readily available in the early 1970s and changed mathematics forever. Not only were these calculators small and easily portable, they substituted for both slide rules and mathematical tables with their ability to store important and commonly used numbers and to use them in complex operations. With clearly labeled buttons and a screen that shows the answer, these calculators were easier to use and required less practice to master. Like slide rules, many modern electronic calculators use logarithms to reduce mathematical operations to repeated operations of addition.

Personal computers are powered by the same type of technology as handheld calculators. Most computers include a software program that simulates the look and feel of a handheld calculator, with buttons that can be clicked with the mouse. The main difference between computers and calculators is that computers are capable of handling complex logical expressions involving unknown values. This basically means that computers are capable of processing more types of information and performing a wider variety of tasks. Making the jump from calculators to computers is an

important technological milestone. Just as people a thousand years ago could not have imagined a small batteryoperated mathematical tool, it is difficult to imagine a technology that will replace electronic calculators and computers.