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Греческая система счисления. Греческая древняя система счисления


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1. Арабские цифры – In this numeral system, a sequence of digits such as 975 is read as a single number, using the position of the digit in the sequence to interpret its value. The symbol for zero is the key to the effectiveness of the system, the system was adopted by Arab mathematicians in Baghdad and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic letters in the Maghreb, the current form of the numerals developed in North Africa, distinct in form from the Indian and eastern Arabic numerals. The use of Arabic numerals spread around the world through European trade, books, the term Arabic numerals is ambiguous. It most commonly refers to the widely used in Europe. Arabic numerals is also the name for the entire family of related numerals of Arabic. It may also be intended to mean the numerals used by Arabs and it would be more appropriate to refer to the Arabic numeral system, where the value of a digit in a number depends on its position. The decimal Hindu–Arabic numeral system was developed in India by AD700, the development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmaguptas formulation of zero as a number in AD628. The system was revolutionary by including zero in positional notation, thereby limiting the number of 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 glyphs most commonly used in conjunction with the Latin script since early modern times are 0123456789. The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the symbol for zero in them, dated back as far as the 6th century AD. Inscriptions in Indonesia and Cambodia dating to AD683 have also been found and their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal system to include fractions. The decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. Ghubar numerals themselves are probably of Roman origin, 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. In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, Algoritmi, the translators rendition of the authors name, gave rise to the word algorithm

2. Бирманские числительные – Burmese numerals are a set of numerals traditionally used in the Burmese language, although the Arabic numerals are also used. Burmese numerals follow the Hindu-Arabic numeral system used in the rest of the world. 1 Burmese for zero comes from Sanskrit śūnya.2 Can be abbreviated to IPA, in list contexts, spoken Burmese has innate pronunciation rules that govern numbers when they are combined with another word, be it a numerical place or a measure word. Other suffixes such as ထောင်, သောင်း, သိန်း, and သန်း all shift to, for six and eight, no pronunciation shift occurs. These pronunciation shifts are exclusively confined to spoken Burmese and are not spelt any differently,1 Shifts to voiced consonant following three, four, five, and nine. Ten to nineteen are almost always expressed without including တစ်, another pronunciation rule shifts numerical place name from the low tone to the creaky tone. Number places from 10 up to 107 has increment of 101, beyond those Number places, larger number places have increment of 107. 1014 up to 10140 has increment of 107, numbers in the hundreds place, shift from ရာ to ရာ့, except for numbers divisible by 100. Numbers in the place, shift from ထောင် to ထောင့်. Hence, a number like 301 is pronounced, while 300 is pronounced, the digits of a number are expressed in order of decreasing digits place. When a number is used as an adjective, the word order is. However, for numbers, the word order is flipped to. The exception to rule is the number 10, which follows the standard word order. Ordinal numbers, from first to tenth, are Burmese pronunciations of their Pali equivalents and they are prefixed to the noun. Beyond that, cardinal numbers can be raised to the ordinal by suffixing the particle မြောက် to the number in the order, number + measure word + မြောက်. Colloquially, decimal numbers are formed by saying ဒသမ where the separator is located. For example,10.1 is ဆယ် ဒသမ တစ်, half is expressed primarily by တစ်ဝက်, although ထက်ဝက်, အခွဲ and အခြမ်း are also used. Quarter is expressed with အစိတ် or တစ်စိတ်, other fractional numbers are verbally expressed as follows, denominator + ပုံ + numerator + ပုံ

3. Китайские числительные – Chinese numerals are words and characters used to denote numbers in Chinese. Today speakers of Chinese use three written numeral systems, the system of Arabic numerals used worldwide, and two indigenous systems, the more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These are shared with languages of the Chinese cultural sphere such as Japanese, Korean. The other indigenous system is the Suzhou numerals, or huama, a positional system and these were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but have been gradually supplanted by Arabic numerals. The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals, similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it not use the positional system as in Arabic numerals. There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, there are two sets of characters for Chinese numerals, one for everyday writing and one for use in commercial or financial contexts known as dàxiě. A forger could easily change the everyday characters 三十 to 五千 just by adding a few strokes and that would not be possible when writing using the financial characters 參拾 and 伍仟. They are also referred to as bankers numerals, anti-fraud numerals, for the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters, S denotes Simplified Chinese characters, in the PLA, some numbers will have altered names when used for clearer radio communications. They are,0, renamed 洞 lit, hole 1, renamed 幺 lit. small 2, renamed 两 lit. Double 7, renamed 拐 lit. cane, kidnap, turn 9, hook For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan. To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are found in ancient texts. Some of the words are still being used today. The following are characters used to denote small order of magnitude in Chinese historically, with the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse. In the Peoples Republic of China, the translations for the SI prefixes in 1981 were different from those used today, the Republic of China defined 百萬 as the translation for mega

4. Японские числительные – The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are based on the Chinese numerals. Two sets of pronunciations for the numerals exist in Japanese, one is based on Sino-Japanese readings of the Chinese characters, there are two ways of writing the numbers in Japanese, in Hindu-Arabic numerals or in Chinese numerals. The Hindu-Arabic numerals are often used in horizontal writing. Numerals with multiple On readings use the Go-on and Kan-on variants respectively, * The special reading 〇 maru is also found. It may be used when reading individual digits of a number one after another. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyū and this usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. However, as a number, it is written as 0 or rei. Additionally, two and five are pronounced with a vowel in phone numbers Starting at 万, numbers begin with 一 if no digit would otherwise precede. That is,100 is just 百 hyaku, and 1000 is just 千 sen and this differs from Chinese as numbers begin with 一 if no digit would otherwise precede starting at 百. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is normally attached before 千 sen and that is,10,000,000 is normally read as 一千万 issenman. But if 千 sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000 and that is,15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, and 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku. The numbers 4 and 9 are considered unlucky in Japanese,4, pronounced shi, is a homophone for death,9, the number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese, in modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in names, day-of-month names. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu, shichi-gatsu, the on readings are also used when shouting out headcounts. Intermediate numbers are made by combining elements, Tens from 20 to 90 are -jū as in 二十 to 九十. Hundreds from 200 to 900 are -hyaku, thousands from 2000 to 9000 are -sen

5. Цифры Сучжоу – The Suzhou numerals, also known as Suzhou mazi or huama, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numeral system is the only surviving variation of the rod numeral system, the rod numeral system is a positional numeral system used by the Chinese in mathematics. Suzhou numerals are a variation of the Southern Song rod numerals, Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have gradually been supplanted by Arabic numerals. This is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics, nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices. In the Suzhou numeral system, special symbols are used for digits instead of the Chinese characters, the digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode. An additional three code points starting from U+3038 were added later, the numbers one, two, and three are all represented by vertical bars. This can cause confusion when they next to each other. Standard Chinese ideographs are often used in this situation to avoid ambiguity, for example,21 is written as 〢一 instead of 〢〡 which can be confused with 3. The first character of such sequences is usually represented by the Suzhou numeral, the full numerical notations are written in two lines to indicate numerical value, order of magnitude, and unit of measurement. Following the rod system, the digits of the Suzhou numerals are always written horizontally from left to right. The first line contains the values, in this example. The second line consists of Chinese characters that represents the order of magnitude, in this case 十元 which stands for ten yuan. When put together, it is read as 40.22 yuan. Zero is represented by the character for zero, leading and trailing zeros are unnecessary in this system. This is very similar to the scientific notation for floating point numbers where the significant digits are represented in the mantissa. Also, the unit of measurement, with the first digit indicator, is aligned to the middle of the numbers row. In the Unicode standard version 3.0, these characters are incorrectly named Hangzhou style numerals, in the episode The Blind Banker of the 2010 BBC television series Sherlock, Sherlock Holmes erroneously refers to the number system as Hangzhou instead of the correct Suzhou

6. Счётные палочки – Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan, Korea, and Vietnam. They are placed horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals and they are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Counting rods were used by ancient Chinese for more two thousand years. In 1954, forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, in 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei. On one of the scripts was written, “当利二月定算”. This is one of the earliest examples of using counting rod numerals in writing, in 1976, a bundle of Western Han counting rods made of bones was unearthed from Qianyang County in Shaanxi. The use of counting rods must predate it, Laozi said a good calculator doesnt use counting rods, the Book of Han recorded, they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces. At first calculating rods were round in section, but by the time of the Sui dynasty triangular rods were used to represent positive numbers. After the abacus flourished, counting rods were abandoned except in Japan, counting rods represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used, generally, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc. while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that one is vertical, ten is horizontal, red rods represent positive numbers and black rods represent negative numbers. Ancient Chinese clearly understood negative numbers and zero, though they had no symbol for the latter, later, a go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. In the same manuscript,405 was transcribed as, with a space in between for obvious reasons, and could in no way be interpreted as 45. In other words, transcribed rod numerals may not be positional, the value of a number depends on its physical position on the counting board. A9 at the rightmost position on the stands for 9. Moving the batch of rods representing 9 to the one position gives 9 or 90

7. Кириллическая система счисления – Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used in the First Bulgarian Empire and by South, the system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. By 1725, Russian Imperial coins had transitioned to Arabic numerals, the Cyrillic numerals may still be found in books written in the Church Slavonic language. The system is an alphabetic system, equivalent to the Ionian numeral system. The order is based on the original Greek alphabet rather than the standard Cyrillic alphabetical order, a separate letter is assigned to each unit, each multiple of ten, and each multiple of one hundred. To distinguish numbers from text, a titlo is drawn over the numbers. Examples, –1706 –7118 To evaluate a Cyrillic number, the values of all the figures are added up, for example, ѰЗ is 700 +7, making 707. If the number is greater than 999, the sign is used to multiply the numbers value, for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 +2000. To produce larger numbers, a sign is used to encircle the number being multiplied. Glagolitic numerals are similar to Cyrillic numerals except that values are assigned according to the native alphabetic order of the Glagolitic alphabet. Glyphs for the ones, tens, and hundreds values are combined to form more precise numbers, for example, ⰗⰑⰂ is 500 +80 +3 or 583. As with Cyrillic numerals, the numbers 11 through 19 are typically written with the ones digit before the glyph for 10, for example ⰅⰊ is 6 +10, early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions

8. Эфиопское письмо – Geez is a script used as an abugida for several languages of Ethiopia and Eritrea. It originated as an abjad and was first used to write Geez, now the language of the Ethiopian Orthodox Tewahedo Church. In Amharic and Tigrinya, the script is often called fidäl, the Geez script has been adapted to write other, mostly Semitic, languages, particularly Amharic in Ethiopia, and Tigrinya in both Eritrea and Ethiopia. It is also used for Sebatbeit, Meen, and most other languages of Ethiopia, in Eritrea it is used for Tigre, and it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geez more than do the other derivative languages, some other languages in the Horn of Africa, such as Oromo, used to be written using Geez, but have migrated to Latin-based orthographies. For the representation of sounds, this uses a system that is common among linguists who work on Ethiopian Semitic languages. This differs somewhat from the conventions of the International Phonetic Alphabet, see the articles on the individual languages for information on the pronunciation. The earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, after the 7th and 6th centuries BC, however, variants of the script arose, evolving in the direction of the Geez abugida. This evolution can be seen most clearly in evidence from inscriptions in Tigray region in northern Ethiopia, at least one of Wazebas coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. It has been argued that the marking pattern of the script reflects a South Asian system. On the other hand, emphatic P̣ait ጰ, a Geez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geez and the South Arabian alphabet, Many of the names are cognate with those of Phoenician. Two alphabets were used to write the Geez language, an abjad and later an abugida. The abjad, used until c.330 AD, had 26 consonantal letters, h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geez is written left to right. The Geez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but slightly irregular way, the original form of the consonant was used when the vowel was ä, the so-called inherent vowel. The resulting forms are shown below in their traditional order, for some consonants, there is an eighth form for the diphthong -wa or -oa, and a ninth for -yä

9. Еврейские цифры – The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BC, the current numeral system is also known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC, in this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit is assigned a letter, each tens a separate letter. The later hundreds are represented by the sum of two or three letters representing the first four hundreds, to represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. In Israel today, the system of Arabic numerals is used in almost all cases. The Hebrew numerals are used only in cases, such as when using the Hebrew calendar, or numbering a list. Numbers in Hebrew from zero to one million, Hebrew alphabet are used to a limited extent to represent numbers, widely used on calendars. In other situations Arabic numerals are used, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender, note, For ordinal numbers greater than 10, cardinal numbers are used instead. Note, For numbers greater than 20, gender does not apply, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. Ordinal numbers must also agree in number and definite status like other adjectives, the cardinal number precedes the noun, except for the number one which succeeds it. The number two is special - shnayim and shtayim become shney and shtey when followed by the noun they count, for ordinal numbers greater than ten the cardinal is used. The Hebrew numeric system operates on the principle in which the numeric values of the letters are added together to form the total. For example,177 is represented as קעז which corresponds to 100 +70 +7 =177, mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to numbers from 500

10. Акшара-санкхья – Ka·ṭa·pa·yā·di system of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of numbers as words or verses. The oldest available evidence of the use of Kaṭapayādi system is from Grahacāraṇibandhana by Haridatta in 683 CE and it has been used in Laghu·bhāskarīya·vivaraṇa written by Śaṅkara·nārāyaṇa in 869 CE. Some argue that the system originated from Vararuci, in some astronomical texts popular in Kerala planetary positions were encoded in the Kaṭapayādi system. The first such work is considered to be the Chandra-vakyani of Vararuci, therefore, sometime in the early first millennium is a reasonable estimate for the origin of the Kaṭapayādi system. Aryabhata, in his treatise Ārya·bhaṭīya, is known to have used a similar, there is no definitive evidence whether the Ka-ṭa-pa-yā-di system originated from Āryabhaṭa numeration. Almost all evidences of the use of Ka-ṭa-pa-yā-di system is from south India, not much is known about its use in north India. However, on a Sanskrit astrolabe discovered in north India, the degrees of the altitude are marked in the Kaṭapayādi system and it is preserved in the Sarasvathy Bhavan Library of Sampurnanand Sanskrit University, Varanasi. The Ka-ṭa-pa-yā-di system is not confined to India, some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma. Following verse found in Śaṅkaravarmans Sadratnamāla explains the mechanism of the system. e, the nine integers are represented by consonant group beginning with ka, ṭa, pa, ya. In a conjunct consonant, the last of the consonants alone will count, a consonant without vowel is to be ignored. Explanation, The assignment of letters to the numerals are as per the following arrangement, consonants have numerals assigned as per the above table. For example, ba is always 3 whereas 5 can be represented by either nga or ṇa or ma or śha, all stand-alone vowels like a and ṛ are assigned to zero. In case of a conjunct, consonants attached to a non-vowel will not be valueless, for example, kya is formed by k + ya + a. The only consonant standing with a vowel is ya, so the corresponding numeral for kya will be 1. There is no way of representing Decimal separator in the system, indians used the Hindu-Arabic numeral system for numbering, traditionally written in increasing place values from left to right. This is as per the rule aṅkānām vāmato gatiḥ which means numbers go from left to right, the consonant, ḷ, present in the Dravidian languages of south India, is employed in works using the Kaṭapayādi system, like Mādhavas sine table. Some practitioners do not map the stand-alone vowels to zero, but, it is sometimes considered valueless. Mādhavas sine table constructed by 14th century Kerala mathematician-astronomer Mādhava of Saṅgama·grāma employs the Kaṭapayādi system to enlist the trigonometric sines of angles, Śaṅkara·varmans Sad·ratna·mālā uses the Kaṭapayādi system

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Греческая система счисления — Википедия

Материал из Википедии — свободной энциклопедии

Системы счисления в культуре Индо-арабская Восточноазиатские Алфавитные Другие Позиционные Смешанные системы Непозиционные
АрабскаяТамильскаяБирманская КхмерскаяЛаосскаяМонгольскаяТайская
КитайскаяЯпонскаяСучжоуКорейская ВьетнамскаяСчётные палочки
АбджадияАрмянскаяАриабхатаКириллическая ГреческаяЭфиопскаяЕврейскаяАкшара-санкхья
ВавилонскаяЕгипетскаяЭтрусскаяРимскаяДунайская АттическаяКипуМайяскаяЭгейскаяСимволы КППУ
2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 60
Нега-позиционная
Симметричная
Фибоначчиева
Единичная (унарная)

Греческая система счисления, также известная как ионийская или новогреческая — непозиционная система счисления. Алфавитная запись чисел, в которой в качестве символов для счёта, употребляют буквы классического греческого алфавита, а также некоторые буквы доклассической эпохи, такие как ϛ (стигма), ϟ (коппа) и ϡ (сампи).

Эта система пришла на смену аттической, или старогреческой, системе, которая господствовала в Греции в III веке до н. э.

Необходимость сохранять порядок букв ради сохранения их числовых значений привела к относительно ранней (IV век до н. э.) стабилизации греческого алфавита.

1 α 10 ι 100 ρ
2 β 20 κ 200 σ
3 γ 30 λ 300 τ
4 δ 40 μ 400 υ
5 ε 50 ν 500 φ
6 ϝ или ϛ 60 ξ 600 χ
7 ζ 70 ο 700 ψ
8 η 80 π 800 ω
9 θ 90 ϟ 900 ϡ

Пример

Данные символы позволяют записать лишь целые числа от 1 до 999, например:

  • 45 — με
  • 632 — χλβ
  • 970 — ϡο

См. также

Видео по теме

Ссылки

  • J. J. O'Connor, E. F. Robertson. Greek number systems. MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland (январь 2001).
  • Титло — программа для перевода греческих ионических чисел

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Аттическая система счисления - WikiVisually

1. Арабские цифры – In this numeral system, a sequence of digits such as 975 is read as a single number, using the position of the digit in the sequence to interpret its value. The symbol for zero is the key to the effectiveness of the system, the system was adopted by Arab mathematicians in Baghdad and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic letters in the Maghreb, the current form of the numerals developed in North Africa, distinct in form from the Indian and eastern Arabic numerals. The use of Arabic numerals spread around the world through European trade, books, the term Arabic numerals is ambiguous. It most commonly refers to the widely used in Europe. Arabic numerals is also the name for the entire family of related numerals of Arabic. It may also be intended to mean the numerals used by Arabs and it would be more appropriate to refer to the Arabic numeral system, where the value of a digit in a number depends on its position. The decimal Hindu–Arabic numeral system was developed in India by AD700, the development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmaguptas formulation of zero as a number in AD628. The system was revolutionary by including zero in positional notation, thereby limiting the number of 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 glyphs most commonly used in conjunction with the Latin script since early modern times are 0123456789. The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the symbol for zero in them, dated back as far as the 6th century AD. Inscriptions in Indonesia and Cambodia dating to AD683 have also been found and their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal system to include fractions. The decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. Ghubar numerals themselves are probably of Roman origin, 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. In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, Algoritmi, the translators rendition of the authors name, gave rise to the word algorithm

2. Бирманские числительные – Burmese numerals are a set of numerals traditionally used in the Burmese language, although the Arabic numerals are also used. Burmese numerals follow the Hindu-Arabic numeral system used in the rest of the world. 1 Burmese for zero comes from Sanskrit śūnya.2 Can be abbreviated to IPA, in list contexts, spoken Burmese has innate pronunciation rules that govern numbers when they are combined with another word, be it a numerical place or a measure word. Other suffixes such as ထောင်, သောင်း, သိန်း, and သန်း all shift to, for six and eight, no pronunciation shift occurs. These pronunciation shifts are exclusively confined to spoken Burmese and are not spelt any differently,1 Shifts to voiced consonant following three, four, five, and nine. Ten to nineteen are almost always expressed without including တစ်, another pronunciation rule shifts numerical place name from the low tone to the creaky tone. Number places from 10 up to 107 has increment of 101, beyond those Number places, larger number places have increment of 107. 1014 up to 10140 has increment of 107, numbers in the hundreds place, shift from ရာ to ရာ့, except for numbers divisible by 100. Numbers in the place, shift from ထောင် to ထောင့်. Hence, a number like 301 is pronounced, while 300 is pronounced, the digits of a number are expressed in order of decreasing digits place. When a number is used as an adjective, the word order is. However, for numbers, the word order is flipped to. The exception to rule is the number 10, which follows the standard word order. Ordinal numbers, from first to tenth, are Burmese pronunciations of their Pali equivalents and they are prefixed to the noun. Beyond that, cardinal numbers can be raised to the ordinal by suffixing the particle မြောက် to the number in the order, number + measure word + မြောက်. Colloquially, decimal numbers are formed by saying ဒသမ where the separator is located. For example,10.1 is ဆယ် ဒသမ တစ်, half is expressed primarily by တစ်ဝက်, although ထက်ဝက်, အခွဲ and အခြမ်း are also used. Quarter is expressed with အစိတ် or တစ်စိတ်, other fractional numbers are verbally expressed as follows, denominator + ပုံ + numerator + ပုံ

3. Китайские числительные – Chinese numerals are words and characters used to denote numbers in Chinese. Today speakers of Chinese use three written numeral systems, the system of Arabic numerals used worldwide, and two indigenous systems, the more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These are shared with languages of the Chinese cultural sphere such as Japanese, Korean. The other indigenous system is the Suzhou numerals, or huama, a positional system and these were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but have been gradually supplanted by Arabic numerals. The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals, similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it not use the positional system as in Arabic numerals. There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, there are two sets of characters for Chinese numerals, one for everyday writing and one for use in commercial or financial contexts known as dàxiě. A forger could easily change the everyday characters 三十 to 五千 just by adding a few strokes and that would not be possible when writing using the financial characters 參拾 and 伍仟. They are also referred to as bankers numerals, anti-fraud numerals, for the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters, S denotes Simplified Chinese characters, in the PLA, some numbers will have altered names when used for clearer radio communications. They are,0, renamed 洞 lit, hole 1, renamed 幺 lit. small 2, renamed 两 lit. Double 7, renamed 拐 lit. cane, kidnap, turn 9, hook For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan. To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are found in ancient texts. Some of the words are still being used today. The following are characters used to denote small order of magnitude in Chinese historically, with the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest have fallen into disuse. In the Peoples Republic of China, the translations for the SI prefixes in 1981 were different from those used today, the Republic of China defined 百萬 as the translation for mega

4. Японские числительные – The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are based on the Chinese numerals. Two sets of pronunciations for the numerals exist in Japanese, one is based on Sino-Japanese readings of the Chinese characters, there are two ways of writing the numbers in Japanese, in Hindu-Arabic numerals or in Chinese numerals. The Hindu-Arabic numerals are often used in horizontal writing. Numerals with multiple On readings use the Go-on and Kan-on variants respectively, * The special reading 〇 maru is also found. It may be used when reading individual digits of a number one after another. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyū and this usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. However, as a number, it is written as 0 or rei. Additionally, two and five are pronounced with a vowel in phone numbers Starting at 万, numbers begin with 一 if no digit would otherwise precede. That is,100 is just 百 hyaku, and 1000 is just 千 sen and this differs from Chinese as numbers begin with 一 if no digit would otherwise precede starting at 百. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is normally attached before 千 sen and that is,10,000,000 is normally read as 一千万 issenman. But if 千 sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000 and that is,15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, and 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku. The numbers 4 and 9 are considered unlucky in Japanese,4, pronounced shi, is a homophone for death,9, the number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese, in modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in names, day-of-month names. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu, shichi-gatsu, the on readings are also used when shouting out headcounts. Intermediate numbers are made by combining elements, Tens from 20 to 90 are -jū as in 二十 to 九十. Hundreds from 200 to 900 are -hyaku, thousands from 2000 to 9000 are -sen

5. Цифры Сучжоу – The Suzhou numerals, also known as Suzhou mazi or huama, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numeral system is the only surviving variation of the rod numeral system, the rod numeral system is a positional numeral system used by the Chinese in mathematics. Suzhou numerals are a variation of the Southern Song rod numerals, Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have gradually been supplanted by Arabic numerals. This is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics, nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices. In the Suzhou numeral system, special symbols are used for digits instead of the Chinese characters, the digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode. An additional three code points starting from U+3038 were added later, the numbers one, two, and three are all represented by vertical bars. This can cause confusion when they next to each other. Standard Chinese ideographs are often used in this situation to avoid ambiguity, for example,21 is written as 〢一 instead of 〢〡 which can be confused with 3. The first character of such sequences is usually represented by the Suzhou numeral, the full numerical notations are written in two lines to indicate numerical value, order of magnitude, and unit of measurement. Following the rod system, the digits of the Suzhou numerals are always written horizontally from left to right. The first line contains the values, in this example. The second line consists of Chinese characters that represents the order of magnitude, in this case 十元 which stands for ten yuan. When put together, it is read as 40.22 yuan. Zero is represented by the character for zero, leading and trailing zeros are unnecessary in this system. This is very similar to the scientific notation for floating point numbers where the significant digits are represented in the mantissa. Also, the unit of measurement, with the first digit indicator, is aligned to the middle of the numbers row. In the Unicode standard version 3.0, these characters are incorrectly named Hangzhou style numerals, in the episode The Blind Banker of the 2010 BBC television series Sherlock, Sherlock Holmes erroneously refers to the number system as Hangzhou instead of the correct Suzhou

6. Счётные палочки – Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan, Korea, and Vietnam. They are placed horizontally or vertically to represent any integer or rational number. The written forms based on them are called rod numerals and they are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Counting rods were used by ancient Chinese for more two thousand years. In 1954, forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, in 1973, archeologists unearthed a number of wood scripts from a Han dynasty tomb in Hubei. On one of the scripts was written, “当利二月定算”. This is one of the earliest examples of using counting rod numerals in writing, in 1976, a bundle of Western Han counting rods made of bones was unearthed from Qianyang County in Shaanxi. The use of counting rods must predate it, Laozi said a good calculator doesnt use counting rods, the Book of Han recorded, they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces. At first calculating rods were round in section, but by the time of the Sui dynasty triangular rods were used to represent positive numbers. After the abacus flourished, counting rods were abandoned except in Japan, counting rods represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used, generally, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc. while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that one is vertical, ten is horizontal, red rods represent positive numbers and black rods represent negative numbers. Ancient Chinese clearly understood negative numbers and zero, though they had no symbol for the latter, later, a go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. In the same manuscript,405 was transcribed as, with a space in between for obvious reasons, and could in no way be interpreted as 45. In other words, transcribed rod numerals may not be positional, the value of a number depends on its physical position on the counting board. A9 at the rightmost position on the stands for 9. Moving the batch of rods representing 9 to the one position gives 9 or 90

7. Кириллическая система счисления – Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used in the First Bulgarian Empire and by South, the system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. By 1725, Russian Imperial coins had transitioned to Arabic numerals, the Cyrillic numerals may still be found in books written in the Church Slavonic language. The system is an alphabetic system, equivalent to the Ionian numeral system. The order is based on the original Greek alphabet rather than the standard Cyrillic alphabetical order, a separate letter is assigned to each unit, each multiple of ten, and each multiple of one hundred. To distinguish numbers from text, a titlo is drawn over the numbers. Examples, –1706 –7118 To evaluate a Cyrillic number, the values of all the figures are added up, for example, ѰЗ is 700 +7, making 707. If the number is greater than 999, the sign is used to multiply the numbers value, for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 +2000. To produce larger numbers, a sign is used to encircle the number being multiplied. Glagolitic numerals are similar to Cyrillic numerals except that values are assigned according to the native alphabetic order of the Glagolitic alphabet. Glyphs for the ones, tens, and hundreds values are combined to form more precise numbers, for example, ⰗⰑⰂ is 500 +80 +3 or 583. As with Cyrillic numerals, the numbers 11 through 19 are typically written with the ones digit before the glyph for 10, for example ⰅⰊ is 6 +10, early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions

8. Греческая система счисления – Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made

9. Эфиопское письмо – Geez is a script used as an abugida for several languages of Ethiopia and Eritrea. It originated as an abjad and was first used to write Geez, now the language of the Ethiopian Orthodox Tewahedo Church. In Amharic and Tigrinya, the script is often called fidäl, the Geez script has been adapted to write other, mostly Semitic, languages, particularly Amharic in Ethiopia, and Tigrinya in both Eritrea and Ethiopia. It is also used for Sebatbeit, Meen, and most other languages of Ethiopia, in Eritrea it is used for Tigre, and it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geez more than do the other derivative languages, some other languages in the Horn of Africa, such as Oromo, used to be written using Geez, but have migrated to Latin-based orthographies. For the representation of sounds, this uses a system that is common among linguists who work on Ethiopian Semitic languages. This differs somewhat from the conventions of the International Phonetic Alphabet, see the articles on the individual languages for information on the pronunciation. The earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, after the 7th and 6th centuries BC, however, variants of the script arose, evolving in the direction of the Geez abugida. This evolution can be seen most clearly in evidence from inscriptions in Tigray region in northern Ethiopia, at least one of Wazebas coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. It has been argued that the marking pattern of the script reflects a South Asian system. On the other hand, emphatic P̣ait ጰ, a Geez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geez and the South Arabian alphabet, Many of the names are cognate with those of Phoenician. Two alphabets were used to write the Geez language, an abjad and later an abugida. The abjad, used until c.330 AD, had 26 consonantal letters, h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geez is written left to right. The Geez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but slightly irregular way, the original form of the consonant was used when the vowel was ä, the so-called inherent vowel. The resulting forms are shown below in their traditional order, for some consonants, there is an eighth form for the diphthong -wa or -oa, and a ninth for -yä

10. Еврейские цифры – The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BC, the current numeral system is also known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC, in this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit is assigned a letter, each tens a separate letter. The later hundreds are represented by the sum of two or three letters representing the first four hundreds, to represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, and hundreds of thousands. In Israel today, the system of Arabic numerals is used in almost all cases. The Hebrew numerals are used only in cases, such as when using the Hebrew calendar, or numbering a list. Numbers in Hebrew from zero to one million, Hebrew alphabet are used to a limited extent to represent numbers, widely used on calendars. In other situations Arabic numerals are used, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender, note, For ordinal numbers greater than 10, cardinal numbers are used instead. Note, For numbers greater than 20, gender does not apply, cardinal and ordinal numbers must agree in gender with the noun they are describing. If there is no such noun, the form is used. Ordinal numbers must also agree in number and definite status like other adjectives, the cardinal number precedes the noun, except for the number one which succeeds it. The number two is special - shnayim and shtayim become shney and shtey when followed by the noun they count, for ordinal numbers greater than ten the cardinal is used. The Hebrew numeric system operates on the principle in which the numeric values of the letters are added together to form the total. For example,177 is represented as קעז which corresponds to 100 +70 +7 =177, mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to numbers from 500

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Греческая система счисления — Википедия (с комментариями)

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Системы счисления в культуре Индо-арабская Восточноазиатские Алфавитные Другие Позиционные Смешанные системы Непозиционные
АрабскаяТамильскаяБирманская КхмерскаяЛаосскаяМонгольскаяТайская
КитайскаяЯпонскаяСучжоуКорейская ВьетнамскаяСчётные палочки
АбджадияАрмянскаяАриабхатаКириллическая ГреческаяЭфиопскаяЕврейскаяАкшара-санкхья
ВавилонскаяЕгипетскаяЭтрусскаяРимскаяДунайская АттическаяКипуМайяскаяЭгейскаяСимволы КППУ
2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 60
Нега-позиционная
Симметричная
Фибоначчиева
Единичная (унарная)

Греческая система счисления, также известная как ионийская или новогреческая — непозиционная система счисления. Алфавитная запись чисел, в которой в качестве символов для счёта, употребляют буквы классического греческого алфавита, а также некоторые буквы доклассической эпохи, такие как ϛ (стигма), ϟ (коппа) и ϡ (сампи).

Эта система пришла на смену аттической, или старогреческой, системе, которая господствовала в Греции в III веке до н.э..

Необходимость сохранять порядок букв ради сохранения их числовых значений привела к относительно ранней (4 век до н. э.) стабилизации греческого алфавита.

1 α 10 ι 100 ρ
2 β 20 κ 200 σ
3 γ 30 λ 300 τ
4 δ 40 μ 400 υ
5 ε 50 ν 500 φ
6 ϛ 60 ξ 600 χ
7 ζ 70 ο 700 ψ
8 η 80 π 800 ω
9 θ 90 ϟ 900 ϡ

Пример

Данные символы позволяют записать лишь целые числа от 1 до 999, например:

  • 45 — με
  • 632 — χλβ
  • 970 — ϡο

См. также

Напишите отзыв о статье "Греческая система счисления"

Ссылки

  • J. J. O'Connor, E. F. Robertson. [www-history.mcs.st-andrews.ac.uk/history/HistTopics/Greek_numbers.html Greek number systems]. MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland (январь 2001).
  • [info-7.ru/Titlo/Titlo.shtml Титло] — программа для перевода греческих ионических чисел

Отрывок, характеризующий Греческая система счисления

Про батарею Тушина было забыто, и только в самом конце дела, продолжая слышать канонаду в центре, князь Багратион послал туда дежурного штаб офицера и потом князя Андрея, чтобы велеть батарее отступать как можно скорее. Прикрытие, стоявшее подле пушек Тушина, ушло, по чьему то приказанию, в середине дела; но батарея продолжала стрелять и не была взята французами только потому, что неприятель не мог предполагать дерзости стрельбы четырех никем не защищенных пушек. Напротив, по энергичному действию этой батареи он предполагал, что здесь, в центре, сосредоточены главные силы русских, и два раза пытался атаковать этот пункт и оба раза был прогоняем картечными выстрелами одиноко стоявших на этом возвышении четырех пушек. Скоро после отъезда князя Багратиона Тушину удалось зажечь Шенграбен. – Вишь, засумятились! Горит! Вишь, дым то! Ловко! Важно! Дым то, дым то! – заговорила прислуга, оживляясь. Все орудия без приказания били в направлении пожара. Как будто подгоняя, подкрикивали солдаты к каждому выстрелу: «Ловко! Вот так так! Ишь, ты… Важно!» Пожар, разносимый ветром, быстро распространялся. Французские колонны, выступившие за деревню, ушли назад, но, как бы в наказание за эту неудачу, неприятель выставил правее деревни десять орудий и стал бить из них по Тушину. Из за детской радости, возбужденной пожаром, и азарта удачной стрельбы по французам, наши артиллеристы заметили эту батарею только тогда, когда два ядра и вслед за ними еще четыре ударили между орудиями и одно повалило двух лошадей, а другое оторвало ногу ящичному вожатому. Оживление, раз установившееся, однако, не ослабело, а только переменило настроение. Лошади были заменены другими из запасного лафета, раненые убраны, и четыре орудия повернуты против десятипушечной батареи. Офицер, товарищ Тушина, был убит в начале дела, и в продолжение часа из сорока человек прислуги выбыли семнадцать, но артиллеристы всё так же были веселы и оживлены. Два раза они замечали, что внизу, близко от них, показывались французы, и тогда они били по них картечью. Маленький человек, с слабыми, неловкими движениями, требовал себе беспрестанно у денщика еще трубочку за это , как он говорил, и, рассыпая из нее огонь, выбегал вперед и из под маленькой ручки смотрел на французов.

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Греческая система счисления — Википедия

Материал из Википедии — свободной энциклопедии

Системы счисления в культуре Индо-арабская Восточноазиатские Алфавитные Другие Позиционные Смешанные системы Непозиционные
АрабскаяТамильскаяБирманская КхмерскаяЛаосскаяМонгольскаяТайская
КитайскаяЯпонскаяСучжоуКорейская ВьетнамскаяСчётные палочки
АбджадияАрмянскаяАриабхатаКириллическаяГреческая ГрузинскаяЭфиопскаяЕврейскаяАкшара-санкхья
ВавилонскаяЕгипетскаяЭтрусскаяРимскаяДунайская АттическаяКипуМайяскаяЭгейскаяСимволы КППУ
2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 60
Нега-позиционная
Симметричная
Фибоначчиева
Единичная (унарная)

Греческая система счисления, также известная как ионийская или новогреческая — непозиционная система счисления. Алфавитная запись чисел, в которой в качестве символов для счёта, употребляют буквы классического греческого алфавита, а также некоторые буквы доклассической эпохи, такие как ϛ (стигма), ϟ (коппа) и ϡ (сампи).

Эта система пришла на смену аттической, или старогреческой, системе, которая господствовала в Греции в III веке до н. э.

Необходимость сохранять порядок букв ради сохранения их числовых значений привела к относительно ранней (IV век до н. э.) стабилизации греческого алфавита.

1 α 10 ι 100 ρ
2 β 20 κ 200 σ
3 γ 30 λ 300 τ
4 δ 40 μ 400 υ
5 ε 50 ν 500 φ
6 ϝ или ϛ 60 ξ 600 χ
7 ζ 70 ο 700 ψ
8 η 80 π 800 ω
9 θ 90 ϟ 900 ϡ

Данные символы позволяют записать лишь целые числа от 1 до 999, например:

  • 45 — με
  • 632 — χλβ
  • 970 — ϡο
  • J. J. O'Connor, E. F. Robertson. Greek number systems. MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland (январь 2001).
  • Титло — программа для перевода греческих ионических чисел

ru.wikiyy.com

Греческая система счисления - это... Что такое Греческая система счисления?

Системы счисления в культуре Индо-арабская система счисления Восточноазиатские системы счисления Алфавитные системы счисления Другие системы Позиционные системы счисления Смешанные системы счисления Непозиционные системы счисления
АрабскаяИндийскиеТамильскаяБирманская КхмерскаяЛаоскаяМонгольскаяТайская
КитайскаяЯпонскаяСучжоуКорейская ВьетнамскаяСчётные палочки
АбджадияАрмянскаяАриабхатаКириллическая ГреческаяЭфиопскаяЕврейскаяКатапаяди
ВавилонскаяЕгипетскаяЭтрускаяРимская АттическаяКипуМайская
Десятичная система счисления (10)
2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 20, 60
Нега-позиционная система счисления
Симметричная система счисления
Фибоначчиева система счисления
Единичная (унарная) система счисления
Список систем счисления

Греческая система счисления, также известная как ионийская или новогреческая — непозиционная система счисления, в которой, в качестве символов для счёта, употребляют греческие буквы, а также дополнительные символы, такие как ς (стигма), Ϙ (копа) и Ϡ (сампи).

Эта система пришла на смену аттической, или старогреческой, системе, которая господствовала в Греции в III веке до н.э..

Необходимость сохранять порядок букв ради сохранения их числовых значений привела к относительно ранней (4 век до н.э.) стабилизации греческого алфавита.

1 α 10 ι 100 ρ
2 β 20 κ 200 σ
3 γ 30 λ 300 τ
4 δ 40 μ 400 υ
5 ε 50 ν 500 φ
6 ς 60 ξ 600 χ
7 ζ 70 ο 700 ψ
8 η 80 π 800 ω
9 θ 90 Ϙ 900 Ϡ

Пример

Данные символы позволяют записать числа лишь от 1 до 999, например:

  • 45 — με
  • 632 — χλβ
  • 970 — Ϡο

Программы

  • Титло — программа для перевода греческих ионических чисел

См. также

dvc.academic.ru

Греческая система счисления — Википедия (с комментариями)

Материал из Википедии — свободной энциклопедии

Системы счисления в культуре Индо-арабская Восточноазиатские Алфавитные Другие Позиционные Смешанные системы Непозиционные
АрабскаяТамильскаяБирманская КхмерскаяЛаосскаяМонгольскаяТайская
КитайскаяЯпонскаяСучжоуКорейская ВьетнамскаяСчётные палочки
АбджадияАрмянскаяАриабхатаКириллическая ГреческаяЭфиопскаяЕврейскаяАкшара-санкхья
ВавилонскаяЕгипетскаяЭтрусскаяРимскаяДунайская АттическаяКипуМайяскаяЭгейскаяСимволы КППУ
2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 60
Нега-позиционная
Симметричная
Фибоначчиева
Единичная (унарная)

Греческая система счисления, также известная как ионийская или новогреческая — непозиционная система счисления. Алфавитная запись чисел, в которой в качестве символов для счёта, употребляют буквы классического греческого алфавита, а также некоторые буквы доклассической эпохи, такие как ϛ (стигма), ϟ (коппа) и ϡ (сампи).

Эта система пришла на смену аттической, или старогреческой, системе, которая господствовала в Греции в III веке до н.э..

Необходимость сохранять порядок букв ради сохранения их числовых значений привела к относительно ранней (4 век до н. э.) стабилизации греческого алфавита.

1 α 10 ι 100 ρ
2 β 20 κ 200 σ
3 γ 30 λ 300 τ
4 δ 40 μ 400 υ
5 ε 50 ν 500 φ
6 ϛ 60 ξ 600 χ
7 ζ 70 ο 700 ψ
8 η 80 π 800 ω
9 θ 90 ϟ 900 ϡ

Пример

Данные символы позволяют записать лишь целые числа от 1 до 999, например:

  • 45 — με
  • 632 — χλβ
  • 970 — ϡο

См. также

Напишите отзыв о статье "Греческая система счисления"

Ссылки

  • J. J. O'Connor, E. F. Robertson. [http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Greek_numbers.html Greek number systems]. MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland (январь 2001).
  • [http://info-7.ru/Titlo/Titlo.shtml Титло] — программа для перевода греческих ионических чисел

Отрывок, характеризующий Греческая система счисления

– О, нет, конечно! Я наверное сюда по ошибке попала. – Совершенно искренне сказала девчушка. – А знаешь, что самое интересное? Из этого «этажа» мы можем ходить везде, а из других никто не может попасть сюда... Правда – интересно?.. Да, это было очень странно и очень захватывающе интересно для моего «изголодавшегося» мозга, и мне так хотелось узнать побольше!.. Может быть потому, что до этого дня мне никогда и никто ничего толком не объяснял, а просто иногда кто-то что-то давал (как например, мои «звёздные друзья»), и поэтому, даже такое, простое детское объяснение уже делало меня необычайно счастливой и заставляло ещё яростнее копаться в своих экспериментах, выводах и ошибках... как обычно, находя во всём происходящем ещё больше непонятного. Моя проблема была в том, что делать или создавать «необычное» я могла очень легко, но вся беда была в том, что я хотела ещё и понимать, как я это всё создаю... А именно это пока мне не очень-то удавалось... – А остальные «этажи»? Ты знаешь, сколько их? Они совсем другие, непохожи на этот?.. – не в состоянии остановиться, я с нетерпением заваливала Стеллу вопросами. – Ой, я тебе обещаю, мы обязательно пойдём туда погулять! Ты увидишь, как там интересно!.. Только там и опасно тоже, особенно в одном. Там такие чудища гуляют!.. Да и люди не очень приятные тоже. – Я думаю, я уже видела похожих чудищ, – кое-что вспомнив, не очень уверенно сказала я. – Вот посмотри... И я попробовала показать ей первых, встреченных в моей жизни, астральных существ, которые нападали на пьяного папу малышки Весты. – Ой, так это же такие же! А где ты их видела? На Земле?!.. – Ну, да, они пришли, когда я помогала одной хорошей маленькой девочке проститься со своим папой... – Значит, они приходят и к живым?.. – очень удивилась моя подружка. – Не знаю, Стелла. Я ещё вообще почти ничего не знаю... А так хотелось бы не ходить в потёмках и не узнавать всё только на «ощупь»... или из своего опыта, когда постоянно за это «бьют по голове»... Как ты думаешь, твоя бабушка не научила бы чему-то и меня?.. – Не знаю... Ты, наверное, должна сама у неё об этом спросить?

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