A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, number may refer to a symbol, a word, or a mathematical abstraction. Read more...
In the future I will continue to index my own number coloring pages here for those of you who are interested in printing and coloring these with your little ones.
Our numerals as we now use them are commonly known as the Hindu-Arabic numerals. Most historical evidence points to India as the country of their origin. To the Arabs who were instrumental in their transmission to Europe, they were known as the "Hindu numbers. " Considerable material on early Hindu numerals is available from manuscripts and inscriptions. Although there is some difference of opinion among the scholars, it seems plausible that the number symbols from which our present digits have developed belonged "to the Brahmi branch of numerals. This was originally a ciphered numeral system with the following first nine symbols:
In the future I will continue to index my own number coloring pages here for those of you who are interested in printing and coloring these with your little ones.
Our numerals as we now use them are commonly known as the Hindu-Arabic numerals. Most historical evidence points to India as the country of their origin. To the Arabs who were instrumental in their transmission to Europe, they were known as the "Hindu numbers. " Considerable material on early Hindu numerals is available from manuscripts and inscriptions. Although there is some difference of opinion among the scholars, it seems plausible that the number symbols from which our present digits have developed belonged "to the Brahmi branch of numerals. This was originally a ciphered numeral system with the following first nine symbols:
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| Brahmi Symbols (100 B.C.) |
The use of a positional system with a zero seems to have made its appearance in India in the period a.d. 600-800.
Around a.d. 800 the system was known among the Arabs in Bagdad and it gradually superseded the older type Arabic numerals. One of the greatest Arab mathematicians of this time was Mohammed ibn Musa al-Khowarizmi, whose work, Al-Jabr wal-Muqabalah, contributed much to the spread of calculations with the new system, first in the Arab world and later in Europe. This treatise is of interest also because it is believed that its title Al-Jabr has given rise to the term algebra of modern mathematics.
Through the Arabs the Hindu numerals were introduced in Europe An interesting early form, the Gobar numerals, appeared in Spain. The name Gobar, or dust, numerals is derived from the Indian custom of calculating on the ground or on a board covered with sand The earliest preserved manuscript using Gobar numerals dates from a.d. 976. The Gobar numerals can also be found on the apices or jetons introduced by Gerbert, later Pope Sylvester II (died a.d. 1003), for calculations on the abacus.
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| Gobar or Western Arabic Numbers (1000 A.D.) |
The works of al-Khowarizmi were translated into Latin, and through a perversion of his name the art of computing with Hindu- Arabic numerals became known as algorism. This term took on various other forms; in Chaucer it appears as augrime. The word is still preserved in mathematics, where a repeated calculating process is called an algorism. Other terms have been taken over from the Arabs. The Hindus early denoted the zero by a dot or a circle and used the term sunya, or the void, for it. Translated into Arabic this became as-sifi, which is the common root of the words zero and cipher.
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Both names are corruptly written: Arsemetrick Arithmetic,
as the Greeks call it, and Augrime for Algorisme as the
Arabians found it; which both betoken the Science of Num-
bring, for Arithmos in Greek is called number: and of it
comes Artithmetick, the Art of Numbring. So that Arith-
metick is a Science or Art teaching the Manner and Use of
Numbring: This Art may be wrought diversely, with Pen or
with Counters. But I first show you the working with the Pen,
and then the other in order.
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During the eleventh and twelfth centuries a number of European scholars went to Spain to study Arab learning. Among them one should mention the Englishmen Robert of Chester and Athelard of Bath, both of whom made translations of al-Khowarizmi's works. Still more important for the spread of the new numerals was the Liber abaci (a.d. 1202), a compendium of arithmetic, algebra, and number theory by Leonardo Fibonacci or Pisano, the only outstanding European mathematician of the Middle Ages. He expresses himself strongly in favor of calculations "modi Indorum," which he learned as a boy from Arab teachers in North Africa before returning to his native town of Pisa. Another text which was widely studied was the Algorismus of John of Halifax or Sacrobosco (about a.d. 1250).
Through the works of these and other scholars, but probably even more through merchants and trade, the knowledge of the Hindu-Arabic numerals was disseminated. The numerals took a great variety of shapes, some quite different from those now in use, but through the introduction of printing the forms became standardized and have since remained almost unchanged.
The transition to the new numerals was a long-drawn-out process. For several centuries there was considerable ill feeling between the algorismists, the users of the new numerals, and the abacists, who adhered to the abacus and the Roman numerals. Tradition long preserved Roman numerals in bookkeeping, coinage, and inscriptions. Not until the sixteenth century had the new numerals won a complete victory in schools and trade. Even as late as the famous work of Nikolaus Copernicus (died a.d. 1543) on the solar system, De revolutionibus orbium coelestium, one finds a strange mixture of Roman and Hindu- Arabic numerals and even numbers written out fully in words. The abacus or counter method of calculation remained in use much longer. To illustrate, let us quote from The Ground of Artes (1540) by Robert Recorde, one of the Englishmen who had most influence on arithmetic:
Both names are corruptly written: Arsemetrick for Arithmetic, as the Greeks call it, and Augrime for Algorisme as the Arabians found it; which both betoken the Science of Numbring, for Arithmos in Greek is called number: and of it comes Arithmetick, the Art of Numbring. So that Arithmetick is a Science or Art teaching the Manner and Use of Numbring: This Art may be wrought diversely, with Pen or with Counters. But I will first show you the working with the Pen, and then the other in order.
To complete this brief sketch of the development of our number system, it should be mentioned that the first satisfactory exposition of the use of decimal fractions was given by the Flemish. Ore