Arabic numerals: Difference between revisions

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Arabic numerals, in common usage, means representation of the digits of the decimal system by the signs 0 1 2 3 4 5 6 7 8 9.

The name, however, is imprecise, for two reasons. First, these digits themselves were borrowed by the Europeans from the Arabs only shortly after the Arabs themselves copied them from the Indians. And secondly, the European digit shapes have changed much from their Arabic originals. Therefore, "Arabic-Indian" better describes the source of the numerals, while "European" better describes the area of their real-world usage. In Arabic usage, the digits (which are called "Indian numerals") have changed less.

In 1202, Fibonacci introduced the decimal system and Arabic numerals to Europe and promoted them with his book Liber Abaci.

In Japan, where the western numerals and alphabet are widely used, the arabic numerals are known as "romanji". Confusingly enough, this translates roughly as "Roman numerals" which conventionally has another meaning altogether.

European, Arabic and Indic numerals

Using Arabic-Indic digits, numbers are written with the most significant digit on the left, just like it is with European digits.

External links:

Unicode reference glyphs for Arabic (See code U+0660-U+0669, U+06F0-U+06F9)
Unicode reference glyphs for Devanagari (See code U+0966-U+096F)
Unicode reference glyphs for Tamil (See code U+0BE6-U+0BEF)

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 '''Arabic numerals''', in common usage, means representation of the [[digit|digits]] of the [[decimal]] system by the signs 0 1 2 3 4 5 6 7 8 9.
+The name, however, is imprecise, for two reasons.
-However, it would be inaccurate to think of this number system just in terms of decimal, rather, it is a completely well-defined system of numbers that pertains to any base, and not just base ten (decimal).
+First, these digits themselves were borrowed by the Europeans from the Arabs only shortly after
+the Arabs themselves copied them from the Indians.
+And secondly, the European digit shapes have changed much from their Arabic originals.
+Therefore, "Arabic-Indian" better describes the source of the numerals, while "European" better
+describes the area of their real-world usage. In Arabic usage, the digits (which are called "Indian numerals") have changed less.
+In [[1202]], [[Fibonacci]] introduced the decimal system and Arabic numerals to Europe and promoted them with his book ''[[Liber Abaci]]''.
-The mathematician who is generally considered the inventor of this numbering system is [[Al-Khwarizmi]], who was not actually an Arab himself, but an [[Iran]]ian [[Muslim]] who published most of his works in the Arabic language, the de facto scientific language of that time.
+In Japan, where the western numerals and alphabet are widely used, the arabic numerals are known as "romanji".  Confusingly enough, this translates roughly as "[[Roman numerals]]" which conventionally has another meaning altogether.
-For instance, when we write 125, today, by default, we assume 125 in base 10, or decimal, and this is how it is constructed:
-x10<sup>0</sup> + 2x10<sup>1</sup> + 1x10<sup>2</sup>  == 5 + 20 + 100 == 125  (in decimal)
-but if we were talking about 125 in base 8, then it would be:
-x8<sup>0</sup> + 2x8<sup>1</sup> + 1x8<sup>2</sup> = 5 + 16 + 64 = 85 (in decimal)
-so  125 in base 10 (decimal) = 125 (decimal)
-but 125 in base  8 (octal) = 85 (decimal)
-For a given base N, there are N symbols of representation. So in base 10 there are 10 symbols, that in most countries 0, 1, 2 ... 9 are used, but the symbols themselves are just symbols, and any symbols could be used, without changing the fundamental concept.  So for instance, instead of using "0,1, 2, 3, 4, 5, 6, 7, 8, 9" for the 10 symbols of base 10, we could use "a, b, c, d, e, f, g, h, i, j" instead .... and in that case, then "125" in base 10, would be written as "bcf", but the numeric value of that number, and also how it is worked out in this number system, would reamin unchanged.
-The binary system (base 2) that we use in computers today is simply the base 2 of this system.  So in base two, there are only two symbols of representation, which normally "0" and "1" are used:
-in binay = 1x2<sup>0</sup> + 0x2<sup>1</sup> + 0x2<sup>2</sup> + 1x2<sup>3</sup> + 1x2<sup>4</sup> = 1+0+0+8+16 = 25 (decimal)
-This number system is the most fundamental and perhaps the greatest inventions of all time which forever changed the way humans think about numbers, and is the foundation of our scientific and mathematical world as we know it today.
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 <table border=1>
 <caption>European, Arabic and Indic numerals</caption>