The Suzhou numerals, 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, 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 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 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
Quipus, sometimes known as khipus or talking knots, were recording devices historically used in a number of cultures and particularly in the region of Andean South America. A quipu usually consisted of colored and plied thread or strings made from cotton or camelid fiber. For the Inca, the system aided in collecting data and keeping records, ranging from monitoring tax obligations, properly collecting census records, calendrical information, the cords contained numeric and other values encoded by knots in a base ten positional system. A quipu could have only a few or up to 2,000 cords, the configuration of the quipus have been compared to string mops. Archaeological evidence has shown a use of finely carved wood as a supplemental. A relatively small number have survived, objects that can be identified unambiguously as quipus first appear in the archaeological record in the first millennium AD. As the region was subsumed under the invading Spanish Empire, the use of the quipu faded from use, however, in several villages, quipu continued to be important items for the local community, albeit for ritual rather than recording use.
It is unclear as to where and how many intact quipus still exist, as many have been stored away in mausoleums, quipu is the Spanish spelling and the most common spelling in English. Khipu is the word for knot in Cusco Quechua, the kh is an aspirated k, in most Quechua varieties, the term is kipu. The word khipu, meaning knot or to knot, comes from the Quechua language word, quipu,1704, most information recorded on the quipus consists of numbers in a decimal system. In the early years of the Spanish conquest of Peru, Spanish officials often relied on the quipus to settle disputes over local tribute payments or goods production, Spanish chroniclers concluded that quipus were used primarily as mnemonic devices to communicate and record numerical information. Quipucamayocs could be summoned to court, where their bookkeeping was recognised as valid documentation of past payments, some of the knots, as well as other features, such as color, are thought to represent non-numeric information, which has not been deciphered.
It is generally thought that the system did not include phonetic symbols analogous to letters of the alphabet, however Gary Urton has suggested that the quipus used a binary system which could record phonological or logographic data. To date, no link has yet been found between a quipu and Quechua, the language of the Peruvian Andes. This suggests that quipus are not a writing system and have no phonetic referent. If this conjecture is correct, quipus are the known example of a complex language recorded in a 3-D system. Marcia and Robert Ascher, after having analyzed several hundred quipus, have shown that most information on quipus is numeric, and these numbers can be read. Each cluster of knots is a digit, and there are three types of knots, simple overhand knots, long knots, consisting of an overhand knot with one or more additional turns
Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient China, Japan 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 and horizontal forms are alternately used, vertical rod numbers are used for the position for the units, ten thousands, etc. while horizontal rod numbers are used for the tens, 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
Burmese numerals are a set of numerals traditionally used in the Burmese language, although the Arabic numerals are 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 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 used. Quarter is expressed with အစိတ် or တစ်စိတ်, other fractional numbers are verbally expressed as follows, denominator + ပုံ + numerator + ပုံ
Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were famous for their observations and calculations. Neither of the predecessors was a positional system and this system first appeared around 2000 BC, its structure reflects the decimal lexical numerals of Semitic languages rather than Sumerian lexical numbers. However, the use of a special Sumerian sign for 60 attests to a relation with the Sumerian system. The Babylonian system is credited as being the first known positional numeral system and this was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base, which can make calculations more difficult. Only two symbols were used to notate the 59 non-zero digits and these symbols and their values were combined to form a digit in a sign-value notation quite similar to that of Roman numerals, for example, the combination represented the digit for 23. A space was left to indicate a place value, similar to the modern-day zero.
Babylonians devised a sign to represent this empty place and they lacked a symbol to serve the function of radix point, so the place of the units had to be inferred from context, could have represented 23 or 23×60 or 23×60×60 or 23/60, etc. A common theory is that 60, a highly composite number, was chosen due to its prime factorization, 2×2×3×5, which makes it divisible by 1,2,3,4,5,6,10,12,15,20. Integers and fractions were represented identically — a radix point was not written, the Babylonians did not technically have a digit for, nor a concept of, the number zero. Although they understood the idea of nothingness, it was not seen as a number—merely the lack of a number, what the Babylonians had instead was a space to mark the nonexistence of a digit in a certain place value. Babylon Babylonia History of zero Numeral system Menninger, Karl W. Number Words and Number Symbols, From Ancient Civilisations to the Computer. CESCNC - a handy and easy-to use numeral converter
The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China.
The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary.
Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
Khmer numerals are the numerals used in the Khmer language. They have been in use since at least the early 7th century, with the earliest known use being on a stele dated to AD604 found in Prasat Bayang, having been derived from the Hindu numerals, modern Khmer numerals represent a decimal positional notation system. It is the script with the first extant material evidence of zero as a figure, dating its use back to the seventh century. However, Old Khmer, or Angkorian Khmer, possessed separate symbols for the numbers 10,20 and this inconsistency with its decimal system suggests that spoken Angkorian Khmer used a vigesimal system. For example,6 is formed from 5 plus 1, with the exception of the number 0, which stems from Sanskrit, the etymology of the Khmer numbers from 1 to 5 is of proto-Mon–Khmer origin. For details of the various alternative romanization systems, see Romanization of Khmer, some authors may alternatively mark as the pronunciation for the word two, and either or for the word three.
In neighbouring Thailand the number three is thought to bring good luck, however, in Cambodia, taking a picture with three people in it is considered bad luck, as it is believed that the person situated in the middle will die an early death. As mentioned above, the numbers from 6 to 9 may be constructed by adding any number between 1 and 4 to the base number 5, so that 7 is literally constructed as 5 plus 2. Beyond that, Khmer uses a base, so that 14 is constructed as 10 plus 4, rather than 2 times 5 plus 4. In constructions from 6 to 9 that use 5 as a base, /pram/ may alternatively be pronounced and this is especially true in dialects which elide /r/, but not necessarily restricted to them, as the pattern follows Khmers minor syllable pattern. The numbers from thirty to ninety in Khmer bear many resemblances to both the modern Thai and Cantonese numbers, informally, a speaker may choose to omit the final and the number is still understood. For example, it is possible to say instead of the full, Language Comparisons, Words in parenthesis indicate literary pronunciations, while words preceded with an asterisk mark are non-productive.
The standard Khmer numbers starting from one hundred are as follows, Although មួយកោដិ is most commonly used to mean ten million, in some areas this is colloquially used to refer to one billion. In order to avoid confusion, sometimes ដប់លាន is used to mean ten million, along with មួយរយលាន for one hundred million, different Cambodian dialects may employ different base number constructions to form greater numbers above one thousand. As a result of prolonged literary influence from both the Sanskrit and Pali languages, Khmer may occasionally use borrowed words for counting. One reason for the decline of numbers is that a Khmer nationalism movement. The Khmer Rouge attempted to cleanse the language by removing all words which were considered politically incorrect, Khmer ordinal numbers are formed by placing the word ទី in front of a cardinal number. This is similar to the use of ที่ thi in Thai and it is generally assumed that the Angkorian and pre-Angkorian numbers represented a dual base system, with both base 5 and base 20 in use
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, Greece uses Arabic numerals, attic numerals, which were 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 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 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
Eastern Arabic numerals
These numbers are known as أرقام هندية in Arabic. They are sometimes called Indic numerals in English, that is sometimes discouraged as it can lead to confusion with Indian numerals, used in Brahmic scripts of India. Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic numeral counterpart, however the variants used with Urdu and other South Asian languages are not encoded separately from the Persian variants. See U+0660 through U+0669 and U+06F0 through U+06F9, written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. There is no conflict unless numerical layout is necessary, as is the case for arithmetic problems and lists of numbers, Eastern Arabic numerals remain strongly predominant vis-à-vis Western Arabic numerals in many countries to the East of the Arab world, particularly in Iran and Afghanistan.
In Pakistan, Western Arabic numerals are more used as a considerable majority of the population is anglophone. Eastern numerals still continue to see use in Urdu publications and newspapers, in North Africa, only Western Arabic numerals are now commonly used. In medieval times, these used a slightly different set
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 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, 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 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, 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
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX.
Both methods appear in documents from the Roman era, even within the same document, double subtractives occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used