|
|
|
Viewing Version
28
of
'Arabic numerals'
|
[ view 'Arabic numerals'
|
back to history
]
| Title of object: |
Arabic numerals |
| Canonical Name: |
ArabicNumerals |
| Type: |
Definition |
| Created on: |
2008-02-18 19:06:14 |
| Modified on: |
2008-02-22 08:07:57 |
| Classification: |
msc:01A35 |
| Keywords: |
1 to 9 |
| Synonyms: |
Arabic numerals=Hindu-Islamic numerals |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
|
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 mapped 1:1 the counting numbers beginning with 1 to alphabetic symbols. Hellene and Greeks ciphered numeral systems established by 2,000 BCE Egyptians. Greeks, for example, ciphered counting numbers excluding zero to Ionian and Doric letter symbols. In the Greek view of number a fraction $1/n$ was written as $n$' an Egyptian ciphered fraction notation.
It should be noted that zero was understood by Greeks, Egyptians and Babylonians, but not as a theoretical counting number. Greeks wrote zero as a oval, topped with two dots. 1500 BCE Egyptians used the word sfr for zero in accounting and other practical 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 several elements of our modern decimal system. Pope Sylvester in 999 CE assisted in popularizing Arab numeration ideas within Egyptian fraction arithmetic a major step that brought abstract numerals to Europe. Fibonacci's 1202 CE Liber Abaci, for example, defined by practical examples medieval arithmetic and medieval higher mathematics. Within the Liber Abaci medieval higher mathematics included lattice multiplication, double false position, indeterminate equations from Diophantus and Chinese Remainder Theorem methods brought from Silk Road trade contacts with China.
The higher medieval math resources may have motivated Renaissance mathematicians to bring together Arab numerals, Arab algorithms, and practical zero ideas together as elements of the decimal system. Zero was 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 popularization of the decimal system with the publication of logarithms and Napier's Bones, an Arab or Hellene lattice multiplication method used by Fibonacci. Napier's numeration publications facilitated several science activities, one being Galileo's 1609 astronomical work.
|
|
|
|
|
|
