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アラビア数字の歴史(サルだからわからんだろ!)

アラビア数字の歴史
(サルだからわからんだろ?)

ローマ数字からアラビア数字に換えたことは、
古代世界から現代世界へビッグジャンプしたのと
同じことだと言っているだろ。

25017で
一の位は 一が7個、
十の位は 十が1個、
百の位は 百が0個ある。☜ここ
千の位は 千が5個、
万の位は 万が2個ある。

「百が0個ある」というのは、
ゼロの概念を導入しているんだぜ。
たとえば、ケーキが2個あるとするだろ。
そのうちの1個を食べると、残りは1個。
残りの1個を食べると、もう「ない」だろ。
アラビア数字は違うんだぜ。
じつは、まだ「0個」あるんだぜ。
これをゼロの概念と言う。
「0の存在を認める」と言うことである。

いいかね、中世ヨーロッパに
アラビア数字がもたらされたから、
科学革命が起こったんだぜ。
そしてこの科学革命によって、
世界史上最強の科学技術文明を
ヨーロッパ人(白人)が作り上げたわけだ。
その科学技術文明の極みが原子爆弾だったわけだ。
その科学技術の粋である原子爆弾を
サルの国(日本)に落としたわけだ。
白人から見れば日本人はサルなんだぜ。



サル「オ…オ…オレはサルなのかぁ~~~~~?」

記数法のかんたんな歴史 ― アレッサンドラ・キング
https://www.youtube.com/watch?v=cZH0YnFpjwU

The Hindu-Arabic number system | Elementary Mathematics (K-6) Explained 4 | NJ Wildberger
https://www.youtube.com/watch?v=y6oS7zE71Dw


Arabic numerals, also called Hindu–Arabic numerals,[1][2] are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The term often implies a number written in the Hindu–Arabic numeral system[3] (where the position of a digit indicates the power of 10 to multiply it by), the most common system for the symbolic representation of numbers in the world today. However, it can also refer to the digits themselves, such as in the statement "octal numbers are written using Arabic numerals."

The Hindu-Arabic numeral system was developed by Indian mathematicians around AD 500.[3] From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west. The current form of the numerals developed in North Africa. It was in the North African city of Bejaia that the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, and colonialism helped popularize the adoption of Arabic numerals around the world.

The term Arabic numerals is ambiguous, it may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals. Although the phrase "Arabic numeral" is frequently capitalized, it is sometimes written in lower case: for instance in its entry in the Oxford English Dictionary,[4] which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.

Other alternative names are Western Arabic numerals, Western numerals, Hindu numerals, and Unicode calls them digits.[5]

Origins[edit]

Main article: History of the Hindu-Arabic numeral system


The numeral "zero" as it appears in two numbers (50 and 270) in an inscription in Gwalior. Dated to the 9th century.[6][7]
The decimal Hindu-Arabic numeral system with zero was developed in India by around AD 700.[8] The development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics. One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which varied regionally.


The numerals used in the Bakhshali manuscript, dated to sometime between the 3rd and 7th century AD.


Modern-day Arab telephone keypad with two forms of Arabic numerals: Western Arabic numerals on the left and Eastern Arabic numerals on the right
The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825 in Arabic, and the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Indian Numerals (Ketab fi Isti'mal al-'Adad al-Hindi) about 830, propagated it in the Arab world. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.[9]

In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952-953. The decimal point notation was introduced by Sind ibn Ali, who also wrote the earliest treatise on Arabic numerals.

Origin of the Arabic numeral symbols[edit]

According to Al-Beruni, there were multiple forms of numerals in use in India, and "Arabs chose among them what appeared to them most useful".[10] Al-Nasawi wrote in the early eleventh century that the mathematicians had not agreed on the form of numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals.[11] The oldest specimens of the written numerals available from Egypt in 260 A.H. (873-874 CE) show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the (Western) Arabic numerals.[12]

Calculations were originally performed using a dust board (takht, Latin: tabula) which involved writing symbols with a stylus and erasing them as part of calculations. Al-Uqlidisi then invented a system of calculations with ink and paper "without board and erasing" (bi-ghayr takht wa-l- ma-w bal bi-daw-t wa-qir-s).[13] The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called -is-b al-hind- in the east, it was called -is-b al-ghub-r in the west (literally, "calculation with dust").[14] The numerals themselves were referred to in the west as ashk-l al‐ghub-r (dust figures, in Ibn al-Y-samin) or qalam al-ghubar (dust letters).[15]

The western Arabic variants of the symbols came to be used in Maghreb and Al-Andalus, which are the direct ancestor of the modern "Arabic numerals" used throughout the world.[16] The divergence in the terminology has led some scholars to propose that the Western Arabic numerals had a separate origin in the so-called "ghub-r numerals" but the available evidence indicates no separate origin.[17] Woepecke has also proposed that the Western Arabic numerals were already in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars.[18][19][20]

Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.[21]


Adoption in Europe[edit]

Evolution of Indian numerals into Arabic numerals and their adoption in Europe

Woodcut showing the 16th century astronomical clock of Uppsala Cathedral, with two clockfaces, one with Arabic and one with Roman numerals.

A German manuscript page teaching use of Arabic numerals (Talhoffer Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer presents them with the Hebrew alphabet and astrology.

Late 18th-century French revolutionary "decimal" clockface.
In 825 Al-Khw-rizm- wrote a treatise in Arabic, On the Calculation with Hindu Numerals,[22] which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum.[23][24] Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm.[25]

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.[26]

From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.

Leonardo Fibonacci (Leonardo of Pisa), a mathematician born in the Republic of Pisa who had studied in Bejaia (Bougie), Algeria, promoted the Indian numeral system in Europe with his 1202 book Liber Abaci:


When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.

The numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement is the same in Arabic as well as the Indo-European languages.

The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the base-10 system (not just these digits) "Hindu numerals",[27][28] referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari:).[21]

The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396,[29] in England, a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral. (See G.F. Hill, The Development of Arabic Numerals in Europe for more examples.) In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456.[30] By the mid-16th century, they were in common use in most of Europe.[31] Roman numerals remained in use mostly for the notation of anno Domini years, and for numbers on clockfaces.

Today, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), for sequential volumes, to differentiate monarchs or family members with the same first names, and (in lower case) to number pages in prefatory material in books.

Adoption in Russia[edit]

Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.




by kabu_kachan | 2019-07-05 21:54 | 科学 | Comments(0)
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