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'Arabic numerals'
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| Title of object: |
Arabic numerals |
| Canonical Name: |
ArabicNumerals |
| Type: |
Definition |
| Created on: |
2008-02-18 19:06:14 |
| Modified on: |
2008-02-21 10:06:39 |
| Classification: |
msc:01A35 |
| Keywords: |
1 to 9 |
| Synonyms: |
Arabic numerals=Hindu-Islamic numerals |
Preamble:
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Content:
Arab mathematicians brought and implemented 1-9 counting numerals from India around 800 CE to replace ciphered numerals. Earlier Arab and Hellene numeration practices had mapped 1:1 the counting numbers, beginning with 1 onto alphabetic symbols. Hellene and Greeks had used ciphered numeral systems established by 2,000 BCE Egyptians. Greeks, for example, ciphered the counting numbers excluding zero onto Ionian and Doric alphabets. In the Greek view of number a fraction $1/n$ was written as $n$' a form of the older Egyptian ciphered fraction notation. Abstract numerals were brought into Europe by 800 CE and later Arab activities.
It should be noted that zero had been understood by Greeks, Egyptians and Babylonians, but not as counting numbers. Greeks wrote zero as a oval, topped with two dots. 1500 BCE Egyptians used the word sfr for zero in accounting and other purposes. Neuegebaur reported that Babylonians used a practical zero around the time of the Egyptian uses.
Arab and East Indian base 10 numeral innovations developed a few of the foundations of our modern decimal system. Pope Sylvester in 999 CE accepted the 800 CE Arab numeration ideas within Egyptian fraction arithmetic a major step that eventually brought abstract numerals and Arab math to Europe. Fibonacci's 1202 CE Liber Abaci, for example, defined the scope of medieval arithmetic and medieval higher mathematics. Within the Liber Abaci medieval higher mathematics included lattice multiplication, indeterminate equations, from Diophantus, and Chinese Remainder Theorem methods brought from Silk Road trade contacts with China.
These higher medieval math resources may have motivated Renaissance mathematicians to bring together Arab numerals, Arab algorithms, and practical zero ideas together to define the base 10 decimal system. Zero was formally added as a theoretical counting number when the base 10 decimal system added an algorithm to the binomial theorem. The well known definition of $$n^0 = 1$$ became an element. The details of the base 10 decimal system were recorded in 1585 CE by Simon Stevin. Stevin used zero as a place-holder and as a theoretical number in two books, one for science and one for business. Both books were approved by the Paris Academy. Several scholars have given credit to Napier for the acceptance and popularization of the decimal system with the development of logarithms and the popularization of Napier's Bones, an Arab or Hellene lattice multiplication method used by Fibonacci. Napier's numeration publications facilitated Galileo's astronomical work in 1609.
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