Introduction to the History of Mathematics (Numeral System) -Joe Ver

8/11/2019 Introduction to the History of Mathematics (Numeral System) -Joe Ver

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Number BasesSome examples of number base systems, some more formalized thanothers, are:

Binary (base 2) Base 2 (Binary)

Hand (base 5) Base 5 (Hand)

Octal (base 8) Base 8 (Octal)

Decimal (base 10) Base 10 (Decimal)

Groupings using 12 (base 12) Base 12 (duodecimal)

Hexadecimal (base 16) Base 16 (Hexadecimal) Mayan (base 20) Base 20 (Vigesimal)

Time and Ancient Sumerian (base 60) Base 60 (Sexagesimal)
http://www.psinvention.com/zoetic/base2.htmhttp://www.psinvention.com/zoetic/base5.htmhttp://www.psinvention.com/zoetic/base8.htmhttp://www.psinvention.com/zoetic/base10.htmhttp://www.psinvention.com/zoetic/base12.htmhttp://www.psinvention.com/zoetic/base16.htmhttp://www.psinvention.com/zoetic/base20.htmhttp://www.psinvention.com/zoetic/base60.htmhttp://www.psinvention.com/zoetic/base60.htmhttp://www.psinvention.com/zoetic/base60.htmhttp://www.psinvention.com/zoetic/base60.htmhttp://www.psinvention.com/zoetic/base20.htmhttp://www.psinvention.com/zoetic/base20.htmhttp://www.psinvention.com/zoetic/base20.htmhttp://www.psinvention.com/zoetic/base16.htmhttp://www.psinvention.com/zoetic/base12.htmhttp://www.psinvention.com/zoetic/base10.htmhttp://www.psinvention.com/zoetic/base8.htmhttp://www.psinvention.com/zoetic/base5.htmhttp://www.psinvention.com/zoetic/base2.htm


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Egyptian numerals A special symbol represents a specified grouping value. For example a (picture

of a hand) represents 5. The Roman numerals and the Egyptian numbering

represent each order of magnitude with a special symbol. Note that this will in

some cases limit how high a numbering system may count because a new

symbol needs to be developed for each successive grouping. For example, the

number 1,475,268 is represented in the Egyptian numbering system as follows:


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Each of the magnitudes of 10 was represented in the above number, for

example the 4 frogs represent 4 hundred thousands and the 5 lotus flowers

represent 5 thousands, etc. In this numbering system, only the magnitudes of

10 that are used are expressed in the written number. The number 5,060 is

thus represented as:


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The Egyptians had a bases 10 system of hieroglyphs for numerals. By

this we mean that they has separate symbols for one unit, one ten, one

hundred, one thousand, one ten thousand, one hundred thousand, and

one million.

Here are the numeral hieroglyphs


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To make up the number 276, for example, fifteensymbols were required: two "hundred" symbols, seven"ten" symbols, and six "unit" symbols. The numbersappeared thus:

276 in hieroglyphs

Here is another example:

4622 in hieroglyphs.


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Roman Numerals

Symbols

Roman numerals are based on seven symbols: a stroke

(identified with the letter I) for a unit, a chevron(identified with the letter V) for a five, a cross-stroke(identified with the letter X) for a ten, a C (identifiedas an abbreviation of Centum) for a hundred, etc.:


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Symbol

c

V

X L

C

D

M

Value

1 (one) (unus)

5 (five) (quinque)

10 (ten) (decem) 50 (fifty) (quinquaginta)

100 (one hundred) (centum)

500 (five hundred)

(quingenti) 1,000 (one thousand) (mille)
http://www.answers.com/topic/i-1http://www.answers.com/topic/v-1http://www.answers.com/topic/xhttp://www.answers.com/topic/lhttp://www.answers.com/topic/c-1http://www.answers.com/topic/d-1http://www.answers.com/topic/m-1http://www.answers.com/topic/1-1http://www.answers.com/topic/fivehttp://www.answers.com/topic/10http://www.answers.com/topic/fiftyhttp://www.answers.com/topic/100-numberhttp://www.answers.com/topic/500-numberhttp://www.answers.com/topic/1000-numberhttp://www.answers.com/topic/1000-numberhttp://www.answers.com/topic/500-numberhttp://www.answers.com/topic/100-numberhttp://www.answers.com/topic/fiftyhttp://www.answers.com/topic/10http://www.answers.com/topic/fivehttp://www.answers.com/topic/1-1http://www.answers.com/topic/m-1http://www.answers.com/topic/d-1http://www.answers.com/topic/c-1http://www.answers.com/topic/lhttp://www.answers.com/topic/xhttp://www.answers.com/topic/v-1http://www.answers.com/topic/i-1


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Symbols are iterated to produce multiples of the decimal

(1, 10, 100, 1,000) values, with V, L, D substituted for a

multiple of five, and the iteration continuing: I "1", II "2", III

"3", V "5", VI "6", VII "7", etc., and the same for other bases:

X "10", XX "20", XXX "30", L "50", LXXX "80"; CC "200",DCC "700", etc.At the fourth iteration, a subtractive

principlemay be employed, with the base placed beforethe

higher base: IIII or IV "4", VIIII or IX "9", XXXX or XL "40",LXXXX or XC "90", CCCC or CD "400", DCCCC or CM

"900".


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The Romans used only what are called capital (upper case) letters in

modern usage. In the Middle Ages, minuscule(lower case) letters were

developed, and these are now also commonly called Roman numerals:

i, ii, iii, iv, etc.Also in medieval use was the substitution ofjfor a final i

to end numbers, such as iijfor 3 or vijfor 7. This was not an additional

symbol, but merely a swashvariant of i.It is used today, especially in

medical prescriptions, to prevent tampering with or misinterpretation

of a number after it is written.

For large numbers (4,000 and above), a bar can be placed above a base

numeral, or parentheses placed around it, to indicate multiplicationby

1,000, although the Romans themselves often just wrote out the "M"s:]
http://www.answers.com/topic/lowercasehttp://www.answers.com/topic/swash-typographyhttp://www.answers.com/topic/r-5http://www.answers.com/topic/multiplicationhttp://www.answers.com/topic/multiplicationhttp://www.answers.com/topic/r-5http://www.answers.com/topic/swash-typographyhttp://www.answers.com/topic/lowercase


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Symbol

V or (V)

X or (X) L or (L)

C or (C)

D or (D)

M or (M)

Value

five thousand ten thousand

fifty thousand

one hundred thousand

five hundred thousand

one million
http://www.answers.com/topic/5000http://www.answers.com/topic/10000-numberhttp://www.answers.com/topic/50000http://www.answers.com/topic/100000-numberhttp://www.answers.com/topic/millionhttp://www.answers.com/topic/millionhttp://www.answers.com/topic/100000-numberhttp://www.answers.com/topic/50000http://www.answers.com/topic/10000-numberhttp://www.answers.com/topic/5000


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The basic multiples of Roman numerals thus

follow a pattern:

Ones

Tens

Hund

reds Thou

sands

Tenthousands

Hund

redthous

ands

1

I

X

C M

X

C

2

II

XX

CC MM

XX

CC

3

III

XXX

CCC MM

M

XXX

CCC

4

IV

XL

CD IV

XL

CD

5

V

L

D

V

L

D

6

VI

LX

DC

VI

LX

DC

7

VII

LXX

DCC

VII

LXX

DCC

8

VIII

LXXX

DCCC

VIII

LXXX

DCCC

9

IX

XC

CM

IX

XC

CM


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A practical way to write a Roman number is to consider themodernArabic numeralsystem, and separately convert thethousands, hundreds, tens, and ones as given in the chart

above. So, for instance, 1234 may be thought of as "onethousand and two hundreds and three tens and four",obtaining M (one thousand) + CC (two hundreds) + XXX(thirty) + IV (four), for MCCXXXIV. Thus eleven is XI (tenand one), 32 is XXXII (thirty and two) and 2009 is MMIX

(two thousand and nine). Note that the subtractiveprinciple is not extended beyond the chart: for example, ILis notused for 49, rather this should be written as forty(XL) and nine (IX), or XLIX.
http://www.answers.com/topic/arabic-numeralshttp://www.answers.com/topic/arabic-numerals


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Chinese-Japanese Multiplicative Grouping

There are characters representing the numbers zerothrough nine, and other characters representing larger numberssuch as tens, hundreds, thousands and so on. There are two sets

of characters for Chinese numerals: one for everyday writing andone for use in commercial or financial contexts known as dxi(simplified Chinese: ; traditional Chinese: ). The latterarose because the characters used for writing numerals aregeometrically simple, so simply using those numerals cannot

prevent forgeries in the same way spelling numbers out inEnglish would. A forger could easily change everyday characters(30) to(5000) by adding just a few strokes. That wouldnot be possible when writing using the financial characters(30) and(5000).
http://en.wikipedia.org/wiki/Simplified_Chinese_charactershttp://en.wikipedia.org/wiki/Traditional_Chinese_charactershttp://en.wiktionary.org/wiki/%E4%B8%89%E5%8D%81http://en.wiktionary.org/wiki/%E4%BA%94%E5%8D%83http://en.wiktionary.org/wiki/%E5%8F%81%E6%8B%BEhttp://en.wiktionary.org/wiki/%E4%BC%8D%E4%BB%9Fhttp://en.wiktionary.org/wiki/%E4%BC%8D%E4%BB%9Fhttp://en.wiktionary.org/wiki/%E5%8F%81%E6%8B%BEhttp://en.wiktionary.org/wiki/%E4%BA%94%E5%8D%83http://en.wiktionary.org/wiki/%E4%B8%89%E5%8D%81http://en.wikipedia.org/wiki/Traditional_Chinese_charactershttp://en.wikipedia.org/wiki/Traditional_Chinese_charactershttp://en.wikipedia.org/wiki/Traditional_Chinese_charactershttp://en.wikipedia.org/wiki/Simplified_Chinese_charactershttp://en.wikipedia.org/wiki/Simplified_Chinese_charactershttp://en.wikipedia.org/wiki/Simplified_Chinese_characters


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Financial

(T) or(S)

(T) or

(S)

(T) or(S)

Normal

(T) or(S)

(T) or(S)

Value

0

1

2

3

4

5

6

7

8

9

10

100

1,000 104

108

Pnyn

lng

y

r

sn

s

w

li

q

b

ji

sh

bi

qin wn

y

Tdenotes Traditional, SdenotesSimplified
http://en.wiktionary.org/wiki/%E9%9B%B6http://en.wiktionary.org/wiki/%E5%A3%B9http://en.wiktionary.org/wiki/%E8%B2%B3http://en.wiktionary.org/wiki/%E8%B4%B0http://en.wiktionary.org/wiki/%E5%8F%84http://en.wiktionary.org/wiki/%E5%8F%81http://en.wiktionary.org/wiki/%E8%82%86http://en.wiktionary.org/wiki/%E4%BC%8Dhttp://en.wiktionary.org/wiki/%E9%99%B8http://en.wiktionary.org/wiki/%E9%99%86http://en.wiktionary.org/wiki/%E6%9F%92http://en.wiktionary.org/wiki/%E6%8D%8Chttp://en.wiktionary.org/wiki/%E7%8E%96http://en.wiktionary.org/wiki/%E6%8B%BEhttp://en.wiktionary.org/wiki/%E4%BD%B0http://en.wiktionary.org/wiki/%E4%BB%9Fhttp://en.wiktionary.org/wiki/%E8%90%AChttp://en.wiktionary.org/wiki/%E5%84%84http://en.wiktionary.org/wiki/%E3%80%87http://en.wiktionary.org/wiki/%E4%B8%80http://en.wiktionary.org/wiki/%E4%BA%8Chttp://en.wiktionary.org/wiki/%E4%B8%89http://en.wiktionary.org/wiki/%E5%9B%9Bhttp://en.wiktionary.org/wiki/%E4%BA%94http://en.wiktionary.org/wiki/%E5%85%ADhttp://en.wiktionary.org/wiki/%E4%B8%83http://en.wiktionary.org/wiki/%E5%85%ABhttp://en.wiktionary.org/wiki/%E4%B9%9Dhttp://en.wiktionary.org/wiki/%E5%8D%81http://en.wiktionary.org/wiki/%E7%99%BEhttp://en.wiktionary.org/wiki/%E5%8D%83http://en.wiktionary.org/wiki/%E8%90%AChttp://en.wiktionary.org/wiki/%E4%B8%87http://en.wiktionary.org/wiki/%E5%84%84http://en.wiktionary.org/wiki/%E4%BA%BFhttp://en.wikipedia.org/wiki/0_(number)http://en.wikipedia.org/wiki/1_(number)http://en.wikipedia.org/wiki/2_(number)http://en.wikipedia.org/wiki/3_(number)http://en.wikipedia.org/wiki/4_(number)http://en.wikipedia.org/wiki/5_(number)http://en.wikipedia.org/wiki/6_(number)http://en.wikipedia.org/wiki/7_(number)http://en.wikipedia.org/wiki/8_(number)http://en.wikipedia.org/wiki/9_(number)http://en.wikipedia.org/wiki/10_(number)http://en.wikipedia.org/wiki/100_(number)http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/10000_(number)http://en.wikipedia.org/wiki/10000_(number)http://en.wikipedia.org/wiki/1_E8http://en.wikipedia.org/wiki/1_E8http://en.wikipedia.org/wiki/1_E8http://en.wikipedia.org/wiki/1_E8http://en.wikipedia.org/wiki/10000_(number)http://en.wikipedia.org/wiki/10000_(number)http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/100_(number)http://en.wikipedia.org/wiki/10_(number)http://en.wikipedia.org/wiki/9_(number)http://en.wikipedia.org/wiki/8_(number)http://en.wikipedia.org/wiki/7_(number)http://en.wikipedia.org/wiki/6_(number)http://en.wikipedia.org/wiki/5_(number)http://en.wikipedia.org/wiki/4_(number)http://en.wikipedia.org/wiki/3_(number)http://en.wikipedia.org/wiki/2_(number)http://en.wikipedia.org/wiki/1_(number)http://en.wikipedia.org/wiki/0_(number)http://en.wiktionary.org/wiki/%E4%BA%BFhttp://en.wiktionary.org/wiki/%E5%84%84http://en.wiktionary.org/wiki/%E4%B8%87http://en.wiktionary.org/wiki/%E8%90%AChttp://en.wiktionary.org/wiki/%E5%8D%83http://en.wiktionary.org/wiki/%E7%99%BEhttp://en.wiktionary.org/wiki/%E5%8D%81http://en.wiktionary.org/wiki/%E4%B9%9Dhttp://en.wiktionary.org/wiki/%E5%85%ABhttp://en.wiktionary.org/wiki/%E4%B8%83http://en.wiktionary.org/wiki/%E5%85%ADhttp://en.wiktionary.org/wiki/%E4%BA%94http://en.wiktionary.org/wiki/%E5%9B%9Bhttp://en.wiktionary.org/wiki/%E4%B8%89http://en.wiktionary.org/wiki/%E4%BA%8Chttp://en.wiktionary.org/wiki/%E4%B8%80http://en.wiktionary.org/wiki/%E3%80%87http://en.wiktionary.org/wiki/%E5%84%84http://en.wiktionary.org/wiki/%E8%90%AChttp://en.wiktionary.org/wiki/%E4%BB%9Fhttp://en.wiktionary.org/wiki/%E4%BD%B0http://en.wiktionary.org/wiki/%E6%8B%BEhttp://en.wiktionary.org/wiki/%E7%8E%96http://en.wiktionary.org/wiki/%E6%8D%8Chttp://en.wiktionary.org/wiki/%E6%9F%92http://en.wiktionary.org/wiki/%E9%99%86http://en.wiktionary.org/wiki/%E9%99%B8http://en.wiktionary.org/wiki/%E4%BC%8Dhttp://en.wiktionary.org/wiki/%E8%82%86http://en.wiktionary.org/wiki/%E5%8F%81http://en.wiktionary.org/wiki/%E5%8F%84http://en.wiktionary.org/wiki/%E8%B4%B0http://en.wiktionary.org/wiki/%E8%B2%B3http://en.wiktionary.org/wiki/%E5%A3%B9http://en.wiktionary.org/wiki/%E9%9B%B6


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Notes is a common informal way to represent zero, but the traditional is more often used in schools.is not a standard Chinese character, because Chinese characters never contain ovals (only boxes).In Unicode,is treated as a Chinese symbol or punctuation, rather than a Chinese ideograph.

also(obsolete financial), can be easily manipulated into(two) or(three).

also(obsolete financial), can be easily manipulated into(one) or(three).also(T) or(S), see Characters with regional usagesection.

also(obsolete financial), can be easily manipulated into(one) or(two).also(T) or(S) sn.

also(obsolete financial)[1]

Although some people useas financial, it is not ideal because it can be easily manipulated into (five) or(thousand).

Chinese numbers group by ten-thousandssee Reading and transcribing numberssection below.

See large numberssection below.
http://en.wikipedia.org/wiki/Template:Unicode_chart_CJK_Symbols_and_Punctuationhttp://en.wikipedia.org/wiki/CJK_Unified_Ideographshttp://en.wiktionary.org/wiki/%E5%BC%8Chttp://en.wiktionary.org/wiki/%E5%BC%8Dhttp://en.wiktionary.org/wiki/%E5%85%A9http://en.wiktionary.org/wiki/%E4%B8%A4http://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wiktionary.org/wiki/%E5%BC%8Ehttp://en.wiktionary.org/wiki/%E5%8F%83http://en.wiktionary.org/wiki/%E5%8F%82http://en.wiktionary.org/wiki/%E4%A6%89http://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wiktionary.org/wiki/%E4%BB%80http://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wiktionary.org/wiki/%E4%BB%80http://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wiktionary.org/wiki/%E4%A6%89http://en.wiktionary.org/wiki/%E5%8F%82http://en.wiktionary.org/wiki/%E5%8F%83http://en.wiktionary.org/wiki/%E5%BC%8Ehttp://en.wikipedia.org/wiki/Chinese_numeralshttp://en.wiktionary.org/wiki/%E4%B8%A4http://en.wiktionary.org/wiki/%E5%85%A9http://en.wiktionary.org/wiki/%E5%BC%8Dhttp://en.wiktionary.org/wiki/%E5%BC%8Chttp://en.wikipedia.org/wiki/CJK_Unified_Ideographshttp://en.wikipedia.org/wiki/Template:Unicode_chart_CJK_Symbols_and_Punctuation


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Whole numbers

Multiple-digit numbers are constructed using a

multiplicative principle; first the digit itself (from 1 to 9), thenthe place (such as 10 or 100); then the next digit.In Mandarin, the multiplier (ling) is often used rather

than (r) for all numbers greater than 200 with the "2"numeral (although as noted earlier this varies from dialect todialect and person to person). Use of both (ling) or (r)

are acceptable for the number 200. When writing in theCantonese dialect, (yi6) is used to represent the "2" numeralfor all numbers. In the southern Min dialect of Chaozhou(Teochew), (no6) is used to represent the "2" numeral in allnumbers from 200 onwards. Thus:
http://en.wiktionary.org/wiki/%E5%85%A9http://en.wiktionary.org/wiki/%E4%BA%8Chttp://en.wiktionary.org/wiki/%E4%BA%8Chttp://en.wiktionary.org/wiki/%E5%85%A9


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Introduction to the History of Mathematics (Numeral System) -Joe Ver

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