Napier Bone

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Timeline of computing hardware 2400 BC–1949 Prehistory 2400 BC–1641 1642-1850 1851–1899 1900–1939 1940–1949 Computing timeline See also References Sources External links 1868 Fingers, Toes, and Pebbles The first tools used as aids to calculation were almost certainly man’s own fingers, and it is not simply a coincidence that the word “digit” is used to refer to a finger (or toe) as well as a numerical quantity. As the need to represent larger numbers grew, early man employed readily available materials for the purpose. Small stones or pebbles could be used to represent larger numbers than fingers and toes and had the added advantage of being able to easily store intermediate results for later use. Thus, it is also no coincidence that the word “calculate” is derived from the Latin word for pebble. Top Bones with Notches

Transcript of Napier Bone

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Timeline of computing hardware 2400 BC–1949

Prehistory 2400 BC–1641 1642-1850 1851–1899 1900–1939 1940–1949 Computing timeline See also References Sources External links

1868

 Fingers, Toes, and Pebbles The first tools used as aids to calculation were almost certainly man’s own fingers, and it is not simply a coincidence that the word “digit” is used to refer to a finger (or toe) as well as a numerical quantity. As the need to represent larger numbers grew, early man employed readily available materials for the purpose. Small stones or pebbles could be used to represent larger numbers than fingers and toes and had the added advantage of being able to easily store intermediate results for later use. Thus, it is also no coincidence that the word “calculate” is derived from the Latin word for pebble.

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 Bones with Notches The oldest objects known to represent numbers are bones with notches carved into them. These bones, which were discovered in Western Europe, date from the Aurignacian period 20,000 to 30,000 years ago and correspond to the first appearance of Cro-Magnon man. (The term Cro-Magnon comes from caves of the same name in Southern France, in which the first skeletons of this race were discovered in 1868.) Of special interest is a wolf’s jawbone more than 20,000 years old with fifty-five notches in groups of five, which was discovered in Czechoslovakia in 1937. This is the

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first evidence of the tally system, which is still used occasionally to the present day and could therefore qualify as one of the most enduring of human inventions.

Also of interest is a piece of bone dating from around 8,500 BC, which was discovered in Africa and which appears to have notches representing the prime numbers 11, 13, 17, and 19. Prime numbers are those that are only wholly divisible by the number one and themselves, so it is not surprising that early man would have attributed a special significance to them. What is surprising is that someone of that era had the mathematical sophistication to recognize this quite advanced concept and took the trouble to write it down – not to mention that prime numbers would appear to have had little relevance to the everyday problems of the time such as gathering food and staying alive.

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2400 BC–1641

Abacus is a Latin word that has its origins in the Greek words abax or abakon (meaning "table" or "tablet") which in turn, possibly originated from the Semitic word abq, meaning "sand" 1.

The Abacus is an ingenious counting device based on the relative positions of two sets of beads moving on parallel strings. The first set contains five beads on each string and allows counting from 1 to 5, while the second set has only two beads per string representing the numbers 5 and 10. The Abacus system seems to be based on a radix of five. Using a radix of five makes sense since humans started counting objects on their fingers.

Why does the abacus exist?

It is difficult to imagine counting without numbers, but there was a time when written numbers did not exist. The earliest counting device was the human hand and its fingers. Then, as larger quantities (larger than ten human-fingers could represent) were counted, various natural items like pebbles and twigs were used to help count. Merchants who traded goods not only needed a way to count goods they bought and sold, but also to calculate the cost of those goods. Until numbers were invented, counting devices were used to make everyday calculations. The abacus is one of many counting devices invented to help count large numbers.

The difference between a counting board and an abacus

It is important to distinguish the early abacuses (or abaci) known as counting boards from the modern abaci. The counting board is a piece of wood, stone or metal with carved

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grooves or painted lines between which beads, pebbles or metal discs were moved. The abacus is a device, usually of wood (plastic, in recent times), having a frame that holds rods with freely-sliding beads mounted on them.

Both the abacus and the counting board are mechanical aids used for counting; they are not calculators in the sense we use the word today. The person operating the abacus performs calculations in their head and uses the abacus as a physical aid to keep track of the sums, the carrys, etc.

What did the first counting board look like?

The earliest counting boards are forever lost because of the perishable materials used in their construction. However, educated guesses can be made about their construction, based on early writings of Plutarch (a priest at the Oracle at Delphi) and others.

In outdoor markets of those times, the simplest counting board involved drawing lines in the sand with ones fingers or with a stylus, and placing pebbles between those lines as place-holders representing numbers (the spaces between 2 lines would represent the units 10s, 100s, etc.). The more affluent people, could afford small wooden tables having raised borders that were filled with sand (usually coloured blue or green). A benefit of these counting boards on tables, was that they could be moved without disturbing the calculation- the table could be picked up and carried indoors.

With the need for portable devices, wooden boards with grooves carved into the surface were then created and wooden markers (small discs) were used as place-holders. The wooden boards then gave way to even more more durable materials like marble and metal (bronze) used with stone or metal markers.

Note: There are comments associated with this question. See the discussion page to add to the conversation.

Read more: http://wiki.answers.com/Q/Who_invented_the_abacus_when#ixzz1CF5EZ7qN

The abacus was invented by the Chinese around 2600. B.C.  It is the oldest known calculating device in history, although the Inca Empire had also devised a system called the Quipu, in which a set of colored

cords in which knots registered the exact figures.

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How does the abacus work?The abacus is used by sliding beads to the center area in order to represent a number. Each row, starting from the right to left, represents ones, tens, hundreds, and so on. Each bead represents a number. The side with with fewer beads assigns the value of 5 to each bead, and the other side's

beads ...

Who is the inventor of abacus?Abacus is the first calculating mechanism known to us, which is basically used for arithmetic operations. It was invented sometime between 1,000 BC and 500 BC by the Babylonians and it was reintroduced by Pope Sylvester II.

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Pope Sylvester II.

Abacus History

While numbers do make the task of counting a lot easier, the practice of using the number system came into existence only a few centuries ago. So how were the people able to count without using numbers in the ancient times? Human fingers were perhaps the oldest tools used for counting, and they were quite useful - until the problem of counting large figures surfaced. In order to make this task convenient, scientists tried to invent tools which could aid mathematical calculations. Abacus was one such ancient tool which was used to count large numbers - a task which was considered to be quite daunting back then.

Before the abacus came into picture, people used various types of counting boards ranging from simple ones, which were made by drawing lines in the sand, to proper wooden or metallic tablets, such as the Salamis tablet used by Babylonians in 300 BC. The abacus, in its present form (sometimes referred to as modern abacus) appeared in China, in the 13th century. This abacus, which was known as suan-pan or 2/5 abacus, had two segments - with the upper segment sporting two beads on each rod, while the lower segment had 5 beads on each rod. The design was eventually modified and several new variants of abacus were introduced, including the Japanese abacus, Korean abacus, etc. The latest version of this classic device - the Lee Kai-chen Abacus was introduced by Lee Kai-chen in 1958. If Lee is to be believed, this abacus makes calculations involving division and multiplication even more easier owing to its unique design.

That was brief information about abacus history, which has always been an issue of raging debate among historians. While most of the historians are of the opinion that abacus was one of the ancient Chinese inventions, there are quite a few historians who trace abacus timeline to the period between 5th and 9th century Europe, from where it was eventually introduced in the East. Distortion is historical accounts is no new thing, and that makes it wiser to depend on various historical sources for information - irrespective of whether it is about abacus history and timeline or history of any other such device.

1614

Napier's bones

Napier's bones is an abacus created by John Napier for calculation of products and quotients of numbers that was based on Arab mathematics and lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab [1] and Fibonacci writing in the Liber Abaci. Also called Rabdology (from Greek ῥάβδoς [r(h)abdos], "rod" and -λογία [logia], "study"). Napier published his version of rods in a work printed in Edinburgh, Scotland, at the end of 1617 entitled Rabdologiæ. Using the multiplication tables embedded in the rods, multiplication can be

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reduced to addition operations and division to subtractions. More advanced use of the rods can even extract square roots. Note that Napier's bones are not the same as logarithms, with which Napier's name is also associated.

The abacus consists of a board with a rim; the user places Napier's rods in the rim to conduct multiplication or division. The board's left edge is divided into 9 squares, holding the numbers 1 to 9. The Napier's rods consist of strips of wood, metal or heavy cardboard. Napier's bones are three dimensional, square in cross section, with four different rods engraved on each one. A set of such bones might be enclosed in a convenient carrying case.

A rod's surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The first square of each rod holds a single digit, and the other squares hold this number's double, triple, quadruple, quintuple, and so on until the last square contains nine times the number in the top square. The digits of each product are written one to each side of the diagonal; numbers less than 10 occupy the lower triangle, with a zero in the top half.

A set consists of 10 rods corresponding to digits 0 to 9. The rod 0, although it may look unnecessary, is obviously still needed for multipliers or multiplicands having 0 in them.

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John Napier

1642Pascal triangle

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Blaise Pascal

Solve This!

Hi my name is Blaise Pascal, I was born on June 19, 1623 in Clermont, France. My mother died when I was three, so my father Etienne Begon raised me. I have two sisters Gilberte and Jacqueline. My father didn’t want me to study math, but I took the math books out of the house and studied the angles of a triangle. I found that the three angles of a triangle equal the sum of two right angles. Then my father said I was ready for math. I began to participate with my father in the Mersennes circle with scientists and mathematicians. My father decided to tutor me himself. I wrote a paper about the “Mystic Hexagon”

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which impressed the members of the circle. One of my sisters wrote a paper saying I was the best mathematician since Archimedes.

 

I had to suspend my association with the Mersennes circle when my sisters and I had to move to Rouen, because my father was appointed Royal tax official in upper Normandy. I had many talents, I was a mathematician, a physicist, and I wrote spiritual papers. Before I was 13 I found an error in René Descartes’ geometry and proved the 32nd proposition of Euclid. My father retired and moved to Paris in 1631. When I was 30 I invented a calculator known as the Pascaline. I invented the Pascaline to help my father with his job as tax official. My machine could do the work of six accountants, and people feared it would be the cause of unemployment. I was disgusted at society’s reactions to my machine so I renounced my interest in math and science, devoting the rest of my life to God. The basic design of the Pascaline lived on in mechanical calculators for 300 years.

In 1653 I was famous for doing the first extensive study of the Pascal triangle. I later on figured out that I hadn’t invented the Pascal triangle, the Chinese invented 300 years ago, before I was alive. In 1654 I resumed my mathematical studies. I studied the theory of probability with Pierre de Fermat because a friend asked me a question about a gambling game. Then I wrote my 18 epistles under a pseudonym. Then in 1658 a terrible pain ached in my tooth while I was about to study the cycloid curve, then I continued my studies and found that the study of math calmed my tooth ache.

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An Arithmometer or Arithmomètre was a mechanical calculator that could add and subtract directly and could perform long multiplications and divisions effectively by using a movable accumulator for the result. Patented in France by Thomas de Colmar in 1820 and manufactured from 1851 to 1915, it became the first commercially successful mechanical calculator[1]. Its sturdy design gave it a strong reputation of reliability and accuracy[2] and made it a key player in the move from human computers to calculating machines that took place during the second half of the 19th century[3].

Its production debut of 1851 launched the mechanical calculator industry[1] which ultimately built millions of machines well into the 1970s. For almost forty years, from 1851 to 1887, the Arithmometer was the only type of mechanical calculator in commercial production and it was sold all over the world. During the later part of that period two companies started manufacturing clones of the Arithmometer, they were: Burkhardt from Germany which started in 1878 and Layton from the UK which started in 1883. Eventually about twenty European companies built clones of the arithmometer until the beginning of WWII

Arithmometer,  early calculating machine, built in 1820 by Charles Xavier Thomas de Colmar of France. Whereas earlier calculating machines, such as Blaise Pascal’s Pascaline in France and Gottfried Wilhelm von Leibniz’s Step Reckoner in Germany, were mere curiosities, with the Industrial Revolution came a widespread need to perform repetitive operations efficiently. With other activities being mechanized, why not calculation? De Colmar effectively met this challenge when he built his Arithmometer, the first commercial mass-produced calculating device. Based on Leibniz’s technology, it could perform addition, subtraction, multiplication, and, with some more elaborate user involvement, division. It was extremely popular and sold for 90 years. In contrast to the modern calculator’s credit-card size, the Arithmometer was large enough to cover a desktop.

Paul A. FreibergerMichael R. Swaine

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1887

Comptometer

Dorr E. Felt

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Patented in the USA by Dorr E. Felt in 1887, the comptometer was the first commercially successful key-driven mechanical calculator. A key-driven calculator is extremely fast because each key adds or subtracts its value to the accumulator as soon as it is pressed and a skilled operator can enter all of the digits of a number simultaneously, using as many fingers as required, making them sometimes faster to use than electronic calculators. Consequently, in specialized applications, comptometers remained in use in limited numbers into the early 1990s, but with the exception of museum pieces, they have all now been superseded by electronic calculators and computers.

Manufactured without interruption from 1887 to the mid 1970s it was constantly improved; first it was made faster and more reliable, then a line of electro-mechanical models was added in the 1930s, but especially it was the first mechanical calculator to receive an all-electronic calculator engine in 1961, with the ANITA Mark VII model released by Sumlock Comptometer, therefore creating the link in between the mechanical and the electronic calculator industries.

Although the comptometer was primarily an adding machine, it could also do subtractions, multiplication and division. Its keyboard consisted of eight or more columns of nine keys each. Special comptometers with varying key arrays were produced for a variety of special purposes, including calculating currency exchanges, times and Imperial weights. The name comptometer was formerly in wide use as a generic name for this class of calculating machine.

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1940Complex Number Calculator

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George Robert Stibitz (April 20, 1904 – January 31, 1995) is internationally recognized as one of the fathers of the modern digital computer. He was a Bell Labs researcher known for his 1930s and 1940s work on the realization of Boolean logic digital circuits using electromechanical relays as the switching element.

Born in York, Pennsylvania, he received his bachelor's degree from Denison University in Granville, Ohio, his master's degree from Union College in 1927, and his Ph.D. in mathematical physics in 1930 from Cornell University.

Contents

[hide] 1 Computer 2 Awards 3 Computer art 4 See also 5 External links

o 5.1 Patents o 5.2 Other

6 References

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[edit] Computer

In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based calculator he dubbed the "Model K" (for "kitchen table", on which he had assembled it), which calculated using binary addition. Bell Labs subsequently authorized a full research program in late 1938 with Stibitz at the helm. Their Complex Number Calculator, completed January 8, 1940, was able to do calculations on complex numbers. In a demonstration to the American Mathematical Society conference at Dartmouth College on September 11, 1940, Stibitz used a teletype to send commands to the Complex Number Calculator in New York over telephone lines. It was the first computing machine ever used remotely over a phone line. (See the commemorative plaque and the hall where this event took place in the photos below.)

Stibitz held 38 patents, in addition to those he earned at Bell Labs. He became a member of the faculty at Dartmouth College in 1964 to build bridges between the fields of computing and medicine, and retired from research in 1983. Replicas of the "Model K" reside in both the Smithsonian Institution and the William Howard Doane Library at Denison University.

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1960

Calculator

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John Atanasoff

An electronic calculator (usually called simply a calculator) is a small, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.

The first electronic calculator was created in the 1960s, building on the history of tools such as the abacus, developed around 2000 BC; and the mechanical calculator, developed in the 17th century. It was developed in parallel with the analog computers of the day.

Pocket-sized devices become available in the 1970s, especially after the invention of the microprocessor developed serendipitously by Intel for a busicom calculator.

Modern calculators are electrically powered (usually by battery and/or solar cell) and vary from cheap, give-away, credit-card sized models to sturdy adding machine-like models with built-in printers. They first became popular in the late 1960s as decreasing size and cost of electronics made possible devices for calculations, avoiding the use of scarce and expensive computer resources. By the 1980s, calculator prices had reduced to a point where a basic calculator was affordable to most. By the 1990s they had become common in math classes in schools, with the idea that students could be freed from basic calculations and focus on the concepts.

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Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, and calculator functions are included in almost all PDA-type devices (save a few dedicated address book and dictionary devices).

In addition to general purpose calculators, there are those designed for specific markets; for example, there are scientific calculators which focus on operations slightly more complex than those specific to arithmetic – for instance, trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher dimensional Euclidean space. They often serve other purposes, however.

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1970First personal computer

Ed Roberts

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A personal computer (PC) is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator. PCs include any type of computer that is used in a "personal" manner. This is in contrast to the batch processing or time-sharing models which allowed large expensive mainframe systems to be used by many people, usually at the same time, or large data processing systems which required a full-time staff to operate efficiently. It is also in contrast with the more recent trend of controlling software availability through an intervening third party such as the Apple App Store.[1][2]

A personal computer may be a desktop computer, a laptop, a tablet PC, or a handheld PC (also called a palmtop). The most common microprocessors in personal computers are x86-compatible CPUs. Software applications for personal computers include word processing, spreadsheets, databases, Web browsers and e-mail clients, games, and myriad personal productivity and special-purpose software applications. Modern personal computers often have connections to the Internet, allowing access to the World Wide Web and a wide range of other resources.

A PC may be used at home or in an office. Personal computers may be connected to a local area network (LAN), either by a cable or a wireless connection.

While early PC owners usually had to write their own programs to do anything useful with the machines, today's users have access to a wide range of commercial and non-commercial software, which is provided in ready-to-run or ready-to-compile form. Since the 1980s, Microsoft and Intel have dominated much of the personal computer market, first with MS-DOS and then with the Wintel platform.