Maya numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal positional numeral system; the numerals are made up of three symbols. For example, thirteen is written as three dots in a horizontal row above two horizontal bars. With these three symbols each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty; the Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of tens. For example, thirty-three would be written as one dot, above three dots atop two bars; the first dot represents "one twenty" or "1×20", added to three dots and two bars, or thirteen. Therefore, + 13 = 33. Upon reaching 202 or 400, another row is started; the number 429 would be written as one dot above one dot above four dots and a bar, or + + 9 = 429. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures; the face glyph for a number represents the deity associated with the number.
These face number glyphs were used, are seen on some of the most elaborate monumental carving. Adding and subtracting numbers below 20 using Maya numerals is simple. Addition is performed by combining the numeric symbols at each level: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. With subtraction, remove the elements of the subtrahend symbol from the minuend symbol: If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol, being worked on; the "Long Count" portion of the Maya calendar uses a variation on the vigesimal numbering. In the second position, only the digits up to 17 are used, the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360, so that one dot over two zeros signifies 360.
This is because 360 is the number of days in a year. Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc; every known example of large numbers in the Maya system uses this'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder; the earliest long count date is from 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero and the Long Count calendar predated the Maya, was the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals were added to the Unicode Standard in June, 2018 with the release of version 11.0. The Unicode block for Mayan Numerals is U+1D2E0–U+1D2FF: Maya Mathematics - online converter from decimal numeration to Maya numeral notation. Anthropomorphic Maya numbers - online story of number representations. BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters
Chinese numerals
Chinese numerals are words and characters used to denote numbers in Chinese. Today, speakers of Chinese use three written numeral systems: the system of Hindu-Arabic numerals used worldwide, 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 other languages of the Chinese cultural sphere such as Japanese and Vietnamese. Most people and institutions in China and Taiwan use the Hindu-Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance for writing amounts on checks, some ceremonial occasions, some boxes, on commercials; the other indigenous system is the Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, in Chinese markets, such as those in Hong Kong before the 1990s, but have been supplanted by Hindu-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 does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not. There are characters representing the numbers zero through nine, other characters representing larger numbers such as tens, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing, known as xiǎoxiě, one for use in commercial or financial contexts, known as dàxiě; the latter arose because the characters used for writing numerals are geometrically simple, so using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could change the everyday characters 三十 to 五千 just by adding a few strokes; that would not be possible when writing using the financial characters 叁拾 and 伍仟. They are referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals".
For the same reason, rod numerals were never used in commercial records. T denotes Traditional Chinese characters. In the People's Liberation Army of the People's Republic of China, 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: renamed 勾 lit. Hook For numbers larger than 10,000 to the long and short scales in the West, there have been four systems in ancient and modern usage; the original one, with unique names for all powers of ten up to the 14th, is ascribed to the Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu. In modern Chinese only the second system is used, in which the same ancient names are used, but each represents a number 10,000 times the previous: In practice, this situation does not lead to ambiguity, with the exception of 兆, which means 1012 according to the system in common usage throughout the Chinese communities as well as in Japan and Korea, but has been used for 106 in recent years.
To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 or 太 instead. Due to this, combinations of 万 and 亿 are used instead of the larger units of the traditional system as well, for example 亿亿 instead of 京; the ROC government in Taiwan uses 兆 to mean 1012 in official documents. Numerals beyond 載 zǎi come from Buddhist texts in Sanskrit, but are found in ancient texts; some of the following words may have transferred meanings. 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 People's Republic of China, the early translation for the SI prefixes in 1981 was different from those used today; the larger and smaller Chinese numerals were defined as translation for the SI prefixes as mega, tera, exa, nano, femto, resulting in the creation of yet more values for each numeral.
The Republic of China defined 百萬 as the translation for 兆 as the translation for tera. This translation is used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz". Today, the governments of both Taiwan use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes; the following table lists the two different standards together with the early translation. Multiple-digit numbers are constructed using a multiplicative principle. In Mandarin, the multiplier 兩 is used rather than 二 for all numbers 200 and greater with the "2" numeral. Use of both 兩 or 二 are acceptabl
Hebrew numerals
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 BCE; the current numeral system is known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca and sometimes known as Hebrew-Aramaic numerals derived from the Egyptian Hieratic numerals. 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, the numeric values for individual letters are added together; each unit is assigned a separate letter, each tens a separate letter, the first four hundreds a separate letter. The 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, hundreds of thousands. Gematria uses these transformations extensively. In Israel today, the decimal system of Arabic numerals is used in all cases; the Hebrew numerals are used only in special cases, such as when using the Hebrew calendar, or numbering a list, much as Roman numerals are used in the West. The Hebrew language has names for common numbers. Letters of the Hebrew alphabet are used to represent numbers in a few traditional contexts, for example in calendars. In other situations Arabic numerals are used. Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine 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. Numbers greater than million were represented by the long scale.
Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine form is used. Ordinal numbers must agree in number and definite status like other adjectives; the cardinal number precedes the noun, except for the number one. 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 additive 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 generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit forms of the Hebrew letters. By convention, the numbers 15 and 16 are represented as ט״ו and ט״ז in order to refrain from using the two-letter combinations י-ה and י-ו, which are alternate written forms for the Name of God in everyday writing.
In the calendar, this manifests every full moon. Combinations which would spell out words with negative connotations are sometimes avoided by switching the order of the letters. For instance, 744 which should be written as תשמ״ד might instead be written as תשד״מ or תמש״ד; the Hebrew numeral system has sometimes been extended to include the five final letter forms—ך, ם, ן, ף and ץ —which are used to indicate the numbers from 500 to 900. The ordinary forms for 500 to 900 are: ת״ק, ת״ר, ת״ש, ת״ת and תת״ק. Gershayim are inserted before the last letter to indicate that the sequence of letters represents a number rather than a word; this is used in the case. A single Geresh is appended after a single letter to indicate that the letter represents a number rather than a word; this is used in the case. Note that Geresh and Gershayim indicate "not a word." Context determines whether they indicate a number or something else. An alternative method found in old manuscripts and still found on modern-day tombstones is to put a dot above each letter of the number.
In print, Arabic numerals are emplo
Mongolian numerals
Mongolian numerals are numerals developed from Tibetan numerals and used in conjunction with the Mongolian and Clear script. They are still used on Mongolian tögrög banknotes; the main sources of reference for Mongolian numerals are mathematical and philosophical works of Janj khutugtu A. Rolbiidorj and D. Injinaash. Rolbiidorj exercises with numerals of up to 1066, the last number which he called “setgeshgui” or “unimaginable” referring to the concept of infinity. Injinaash works with numerals of up to 1059. Of these two scholars, the Rolbiidorj’s numerals, their names and sequencing are accepted and used today, for example, in the calculations and documents pertaining to the Mongolian Government budget. Numbers from 1 to 9 are referred to as "dan", meaning "simple"
Cyrillic numerals
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 by South and East Slavic peoples; the system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. 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 a quasi-decimal alphabetic system, equivalent to the Ionian numeral system but written with the corresponding graphemes of the Cyrillic script; 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, each multiple of one hundred.
To distinguish numbers from text, a titlo is sometimes drawn over the numbers, or they are set apart with dots. The numbers are written as pronounced in Slavonic from the high value position to the low value position, with the exception of 11 through 19, which are written and pronounced with the ones unit before the tens. Examples: – 1706 – 7118To 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 thousands sign is used to multiply the number's value: for example, ҂Ѕ is 6000, while ҂Л҂В is parsed as 30,000 + 2000, making 32,000. To produce larger numbers, a modifying sign is used to encircle the number being multiplied. Two scales existed in such cases, one giving a new name and sign every order of magnitude, the other, each squaring except for the end Glagolitic numerals are similar to Cyrillic numerals except that numeric values are assigned according to the native alphabetic order of the Glagolitic alphabet.
Glyphs for the ones 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 written with the ones digit before the glyph for 10. Whereas Cyrillic numerals use modifying signs for numbers greater than 999, some documents attest to the use of Glagolitic letters for 1000 through 6000, although the validity of 3000 and greater is questioned. Early Cyrillic alphabet Glagolitic alphabet Relationship of Cyrillic and Glagolitic scripts Greek numerals Combining Cyrillic Millions
Eastern Arabic numerals
The Eastern Arabic numerals are the symbols used to represent the Hindu–Arabic numeral system, in conjunction with the Arabic alphabet in the countries of the Mashriq, the Arabian Peninsula, its variant in other countries that use the Perso-Arabic script in the Iranian plateau and Asia. The numeral system originates from an ancient Indian numeral system, re-introduced in the book On the Calculation with Hindu Numerals written by the medieval-era Iranian mathematician and engineer Khwarazmi, whose name was Latinized as Algoritmi; these numbers are known as أرقام هندية in Arabic. They are sometimes called "Indic numerals" in English. However, 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 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 Western Arabic numerals 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, which tend to be justified at the decimal point or comma. Eastern Arabic numerals remain predominant vis-à-vis Western Arabic numerals in many countries to the East of the Arab world in Iran and Afghanistan. In Arabic-speaking Asia as well as Egypt and Sudan both kinds of numerals are used alongside each other with Western Arabic numerals gaining more and more currency, now in traditional countries such as Saudi Arabia; the United Arab Emirates uses both Western Arabic numerals. In Pakistan, Western Arabic numerals are more extensively used as a considerable majority of the population is anglophone.
Eastern numerals still continue to see use in Urdu publications and newspapers, as well as sign boards. In North Africa, only Western Arabic numerals are now used. In medieval times, these areas used a different set
Suzhou numerals
The Suzhou numerals known as Suzhou mazi, is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numerals are known as huama, jingzima and shangma; 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, akin to spelling out the numbers in English. Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have 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 and commerce. 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 +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. Standard Chinese ideographs are 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 represented by the Suzhou numeral, while the second character is represented by the Chinese ideograph. The digits are positional; the full numerical notations are written in two lines to indicate numerical value, order of magnitude, unit of measurement. Following the rod numeral system, the digits of the Suzhou numerals are always written horizontally from left to right when used within vertically written documents; the first line contains the numerical values, in this example, "〤〇〢二" stands for "4022".
The second line consists of Chinese characters that represents the order of magnitude and unit of measurement of the first digit in the numerical representation. In this case "十元" which stands for "ten yuan"; when put together, it is read as "40.22 yuan". Possible characters denoting order of magnitude include: qiān for thousand bǎi for hundred shí for ten blank for oneOther possible characters denoting unit of measurement include: yuán for dollar máo or for 10 cents lǐ for the Chinese mile any other Chinese measurement unitNotice that the decimal point is implicit when the first digit is set at the ten position. Zero is represented by the character for zero. Leading and trailing zeros are unnecessary in this system; this is similar to the modern scientific notation for floating point numbers where the significant digits are represented in the mantissa and the order of magnitude is specified in the exponent. 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 Unicode standard 4.0, an erratum was added which stated: The Suzhou numerals are special numeric forms used by traders to display the prices of goods. The use of "HANGZHOU" in the names is a misnomer. All references to "Hangzhou" in the Unicode standard have been corrected to "Suzhou" except for the character names themselves, which cannot be changed once assigned, according to the Unicode Stability Policy. 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."