Kharosthi
The Kharosthi script spelled Kharoshthi or Kharoṣṭhī, was an ancient Indian script used in Gandhara to write Gandhari Prakrit and Sanskrit. It was popular in Central Asia as well. An abugida, it was introduced at least by the middle of the 3rd century BCE during the 4th century BCE, remained in use until it died out in its homeland around the 3rd century CE, it was in use in Bactria, the Kushan Empire and along the Silk Road, where there is some evidence it may have survived until the 7th century in the remote way stations of Khotan and Niya. Kharosthi is encoded in the Unicode range U+10A00–U+10A5F, from version 4.1. Kharosthi is written right to left, but some inscriptions show the left to right direction, to become universal for the South Asian scripts; each syllable includes the short /a/ sound by default, with other vowels being indicated by diacritic marks. Recent epigraphic evidence highlighted by Professor Richard Salomon of the University of Washington has shown that the order of letters in the Kharosthi script follows what has become known as the Arapacana alphabet.
As preserved in Sanskrit documents, the alphabet runs: a ra pa ca na la da ba ḍa ṣa va ta ya ṣṭa ka sa ma ga stha ja śva dha śa kha kṣa sta jñā rtha bha cha sma hva tsa gha ṭha ṇa pha ska ysa śca ṭa ḍhaSome variations in both the number and order of syllables occur in extant texts. Kharosthi includes only one standalone vowel, used for initial vowels in words. Other initial vowels use the a character modified by diacritics. Using epigraphic evidence, Salomon has established that the vowel order is /a e i o u/, rather than the usual vowel order for Indic scripts /a i u e o/; that is the same as the Semitic vowel order. There is no differentiation between long and short vowels in Kharosthi. Both are marked using the same vowel markers; the alphabet was used in Gandharan Buddhism as a mnemonic for remembering a series of verses on the nature of phenomena. In Tantric Buddhism, the list was incorporated into ritual practices and became enshrined in mantras. There are two special modified forms of these consonants: Various additional marks are used to modify vowels and consonants: Nine Kharosthi punctuation marks have been identified: Kharosthi included a set of numerals that are reminiscent of Roman numerals.
The system is based on an additive and a multiplicative principle, but does not have the subtractive feature used in the Roman number system. The numerals, like the letters, are written from right to left. There is no zero and no separate signs for the digits 5–9. Numbers in Kharosthi use an additive system. For example, the number 1996 would be written as 1000 4 4 1 100 20 20 20 20 10 4 2; the Kharosthi script was deciphered by James Prinsep using the bilingual coins of the Indo-Greek Kingdom. This in turn led to the reading of the Edicts of Ashoka, some of which, from the northwest of South Asia, were written in the Kharosthi script. Scholars are not in agreement as to whether the Kharosthi script evolved or was the deliberate work of a single inventor. An analysis of the script forms shows a clear dependency on the Aramaic alphabet but with extensive modifications to support the sounds found in Indic languages. One model is that the Aramaic script arrived with the Achaemenid Empire's conquest of the Indus River in 500 BCE and evolved over the next 200+ years, reaching its final form by the 3rd century BCE where it appears in some of the Edicts of Ashoka found in northwestern part of South Asia.
However, no intermediate forms have yet been found to confirm this evolutionary model, rock and coin inscriptions from the 3rd century BCE onward show a unified and standard form. An inscription in Aramaic dating back to the 4th century BCE was found in Sirkap, testifying to the presence of the Aramaic script in northwestern India at that period. According to Sir John Marshall, this seems to confirm that Kharoshthi was developed from Aramaic; the study of the Kharosthi script was invigorated by the discovery of the Gandhāran Buddhist texts, a set of birch bark manuscripts written in Kharosthi, discovered near the Afghan city of Hadda just west of the Khyber Pass in Pakistan. The manuscripts were donated to the British Library in 1994; the entire set of manuscripts are dated to the 1st century CE, making them the oldest Buddhist manuscripts yet discovered. Kharosthi was added to the Unicode Standard in March, 2005 with the release of version 4.1. The Unicode block for Kharosthi is U+10A00–U+10A5F: Brahmi History of Afghanistan History of Pakistan Pre-Islamic scripts in Afghanistan Kaschgar und die Kharoṣṭhī Dani, Ahmad Hassan.
Kharoshthi Primer, Lahore Museum Publication Series - 16, Lahore, 1979 Falk, Harry. Schrift im alten Indien: Ein Forschungsbericht mit Anmerkungen, Gunter Narr Verlag, 1993 Fussman's, Gérard. Les premiers systèmes d'écriture en Inde, in Annuaire du Collège de France 1988-1989 Hinüber, Oscar von. Der Beginn der Schrift und frühe Schriftlichkeit in Indien, Franz Steiner Verlag, 1990 Nasim Khan, M.. Ashokan Inscriptions: A Palaeographical Study. Atthariyyat, Vol. I, pp. 131–150. Peshawar Nasim Khan, M.. Two Dated Kharoshthi Inscriptions from Gandhara. Journal of Asian Civilizations, Vol. XXII, No.1, July 1999: 99-103. Nasim Khan, M.. An Inscribed Relic-Casket from Dir; the Journal of Humanities and Social Sciences, Vol. V, No. 1, March 1997: 21-33. Peshawar Nasim Khan, M.. Kharoshthi Inscription from Swabi - Gandhara; the Journal of Humanities and Soc
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"
Roman numerals
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, employ seven symbols, each with a fixed integer value, as follows: The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; the original pattern for Roman numerals used the symbols I, V, X as simple tally marks. Each marker for 1 added a unit value up to 5, was added to to make the numbers from 6 to 9: I, II, III, IIII, V, VI, VII, VIII, VIIII, X; the numerals for 4 and 9 proved problematic, are replaced with IV and IX. This feature of Roman numerals is called subtractive notation; the numbers from 1 to 10 are expressed in Roman numerals as follows: I, II, III, IV, V, VI, VII, VIII, IX, X.
The system being decimal and hundreds follow the same underlying pattern. This is the key to understanding Roman numerals: Thus 10 to 100: X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C. Note that 40 and 90 follow the same subtractive pattern as 4 and 9, avoiding the confusing XXXX. 100 to 1000: C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M. Again - 400 and 900 follow the standard subtractive pattern, avoiding CCCC. In the absence of standard symbols for 5,000 and 10,000 the pattern breaks down at this point - in modern usage M is repeated up to three times; the Romans had several ways to indicate larger numbers, but for practical purposes Roman Numerals for numbers larger than 3,999 are if used nowadays, this suffices. M, MM, MMM. Many numbers include hundreds and tens; the Roman numeral system being decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example: 39 = "Thirty nine" = XXXIX. 246 = "Two hundred and forty six" = CCXLVI. 421 = "Four hundred and twenty one" = CDXXI.
As each power of ten has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin speech, thus: 160 = "One hundred and sixty" = CLX 207 = "Two hundred and seven" = CCVII 1066 = "A thousand and sixty six" = MLXVI. Roman numerals for large numbers are nowadays seen in the form of year numbers, as in these examples: 1776 = MDCCLXXVI. 1954 = MCMLIV 1990 = MCMXC. 2014 = MMXIV (the year of the games of the XXII Olympic Winter Games The current year is MMXIX. The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms problematic. "Classical" inscriptions not infrequently use IIII for "4" instead of IV. Other "non-subtractive" forms, such as VIIII for IX, are sometimes seen, although they are less common.
On the numbered gates to the colosseum, for instance, IV is systematically avoided in favour of IIII, but other "subtractives" apply, so that gate 44 is labelled XLIIII. Isaac Asimov speculates that the use of "IV", as the initial letters of "IVPITER" may have been felt to have been impious in this context. Clock faces that use Roman numerals show IIII for four o'clock but IX for nine o'clock, a practice that goes back to early clocks such as the Wells Cathedral clock of the late 14th century. However, this is far from universal: for example, the clock on the Palace of Westminster, Big Ben, uses a "normal" IV. XIIX or IIXX are sometimes used for "18" instead of XVIII; the Latin word for "eighteen" is rendered as the equivalent of "two less than twenty" which may be the source of this usage. The standard forms for 98 and 99 are XCVIII and XCIX, as described in the "decimal pattern" section above, but these numbers are rendered as IIC and IC originally from the Latin duodecentum and undecentum.
Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX. Most non-standard numerals other than those described above - such as VXL for 45, instead of the standard XLV are modern and may be due to error rather than being genuine variant usage. In the early years 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, while on the north entrance to the Saint Louis Art Museum, 1903 is inscribed as MDCDIII rather than MCMIII. Although Roman numerals came to be written with letters
Decimal
The decimal numeral system is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system; the way of denoting numbers in the decimal system is referred to as decimal notation. A decimal numeral, or just decimal, or casually decimal number, refers to the notation of a number in the decimal numeral system. Decimals may sometimes be identified for containing a decimal separator. "Decimal" may refer to the digits after the decimal separator, such as in "3.14 is the approximation of π to two decimals". The numbers that may be represented in the decimal system are the decimal fractions, the fractions of the form a/10n, where a is an integer, n is a non-negative integer; the decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator. In this context, the decimal numerals with a finite number of non–zero places after the decimal separator are sometimes called terminating decimals.
A repeating decimal is an infinite decimal that after some place repeats indefinitely the same sequence of digits. An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits. Many numeral systems of ancient civilisations use ten and its powers for representing numbers because there are ten fingers on two hands and people started counting by using their fingers. Examples are Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, Chinese numerals. Large numbers were difficult to represent in these old numeral systems, only the best mathematicians were able to multiply or divide large numbers; these difficulties were solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers for forming the decimal numeral system. For writing numbers, the decimal system uses ten decimal digits, a decimal mark, for negative numbers, a minus sign "−".
The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For representing a non-negative number, a decimal consists of either a sequence of digits such as 2017, or in full generality, a m a m − 1 … a 0 or two sequence of digits separated by a decimal mark such as 3.14159, 15.00, or in full generality a m a m − 1 … a 0. B 1 b 2 … b n It is assumed that, if m > 0, the first digit am is not zero, but, in some circumstances, it may be useful to have one or more 0's on the left. This does not change the value represented by the decimal. For example, 3.14 = 03.14 = 003.14. If bn =0, it may be removed, conversely, trailing zeros may be added without changing the represented number: for example, 15 = 15.0 = 15.00 and 5.2 = 5.20 = 5.200. Sometimes the extra zeros are used for indicating the accuracy of a measurement. For example, 15.00 m may indicate that the measurement error is less than one centimeter, while 15 m may mean that the length is fifteen meters, that the error may exceed 10 cm. For representing a negative number, a minus sign is placed before am.
The numeral a m a m − 1 … a 0. B 1 b 2 … b n represents the number a m 10 m + a m − 1 10 m − 1 + ⋯ + a 0 10 0 + b 1 10 1 + b 2 10 2 + ⋯ + b n 10 n Therefore, the contribution of each digit to the value of a number depends on its position in the numeral; that is, the decimal system is a positional numeral system The numbers that are represented by decimal numerals are the decimal fractions, that is, the rational numbers that may be expressed as a fraction, the denominator of, a power of ten. For example, the numerals 0.8, 14.89, 0.00024 represent the fractions 8/10, 1489/100, 24/100000. More a decimal with n digits after the separator represents the fraction with denominator 10n, whose numerator is the integer obtained by removing the separator. Expressed as a reduced fraction, the decimal numbers are those whose denominator is a product of a powe
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."
Arabic numerals
Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It is the most common system for the symbolic representation of numbers in the world today; the Hindu-Arabic numeral system was developed by Indian mathematicians around AD 500 using quite different forms of the numerals. From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west; the current form of the numerals developed in North Africa. It was in the North African city of Bejaia that the Italian scholar Fibonacci first encountered the numerals; the use of Arabic numerals spread around the world through European trade and colonialism. The term Arabic numerals is ambiguous, it may be intended to mean the numerals used by Arabs, in which case it refers to the Eastern Arabic numerals. Although the phrase "Arabic numeral" is capitalized, it is sometimes written in lower case: for instance in its entry in the Oxford English Dictionary, which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.
Alternative names are Western Arabic numerals, Western numerals, Hindu–Arabic numerals, Unicode calls them digits. The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700; the development was gradual, spanning several centuries, but the decisive step was provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten, it is considered an important milestone in the development of mathematics. One may distinguish between this positional system, identical throughout the family, the precise glyphs used to write the numerals, which varied regionally; 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 same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain.
Inscriptions in Indonesia and Cambodia dating to AD 683 have been found. The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825 in Arabic, the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Indian Numerals about 830, propagated it in the Arab world, their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953; the decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus, which are the direct ancestor of the modern "Arabic numerals" used throughout the world.
Woepecke has proposed that the Western Arabic numerals were in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars. 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, which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum. Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm; the first mentions of the numerals in the West are found in the Codex Vigilanus of 976. From the 980s, Gerbert of Aurillac used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth, he was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.
Leonardo Fibonacci, a mathematician born in the Republic of Pisa who had studied in Béjaïa, promoted the Indian numeral system in Europe with his 1202 book Liber Abaci: When my father, appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art soon pleased me above all else and I came to understand it; the numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement is the same in Arabic as well as the Indo-European languages; the reason the digits are more known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were using the digits from Libya to Morocco.
Arabs, on the other hand, call the base-10 system "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabi
Counting rods
Counting rods are small bars 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any rational number; the written forms based on them are called rod numerals. 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. Chinese arithmeticians used counting rods well over two thousand years ago. In 1954 forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, Hunan. In 1973 archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty. On one of the wooden 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-era counting rods made of bones was unearthed from Qianyang County in Shaanxi; the use of counting rods must predate it. 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 cross-section, but by the time of the Sui dynasty mathematicians used triangular rods to represent positive numbers and rectangular rods for negative numbers. After the abacus flourished, counting rods were abandoned except in Japan, where rod numerals developed into a symbolic notation for algebra. Counting rods represent digits by the number of rods, 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 black rods represent negative numbers. Ancient Chinese understood negative numbers and zero, though they had no symbol for the latter; the Nine Chapters on the Mathematical Art, composed in the first century CE, stated " subtract same signed numbers, add different signed numbers, subtract a positive number from zero to make a negative number, subtract a negative number from zero to make a positive number".
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. For instance, in Licheng suanjin, 81 was transcribed as, 108 was transcribed as. In the same manuscript, 405 was transcribed as, with a blank space in between for obvious reasons, could in no way be interpreted as "45". In other words, transcribed rod numerals may not be positional, but on the counting board, they are positional. is an exact image of the counting rod number 405 on a table top or floor. The value of a number depends on its physical position on the counting board. A 9 at the rightmost position on the board stands for 9. Moving the batch of rods representing 9 to the left one position gives 9 or 90. Shifting left again to the third position gives 9 or 900; each time one shifts a number one position to the left, it is multiplied by 10. Each time one shifts a number one position to the right, it is divided by 10.
This applies to multiple-digit numbers. Song dynasty mathematician Jia Xian used hand-written Chinese decimal orders 步十百千萬 as rod numeral place value, as evident from a facsimile from a page of Yongle Encyclopedia, he arranged 七萬一千八百二十四 as 七一八二四 萬千百十步He treated the Chinese order numbers as place value markers, 七一八二四 became place value decimal number. He wrote the rod numerals according to their place value: In Japan, mathematicians put counting rods on a counting board, a sheet of cloth with grids, used only vertical forms relying on the grids. An 18th-century Japanese mathematics book has a checker counting board diagram, with the order of magnitude symbols "千百十一分厘毛“. Examples: Rod numerals are a positional numeral system made from shapes of counting rods. Positive numbers are written as they are and the negative numbers are written with a slant bar at the last digit; the vertical bar in the horizontal forms 6–9 are drawn shorter to have the same character height. A circle is used for 0. Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some think it was created from the Chinese text space filler "□", others think that the Indians acquired it from China, because it resembles a Confucian philosophical symbol for nothing.
In the 13th century, Southern Song mathematicians changed digits for 4, 5, 9 to reduce strokes. The new horizontal forms transformed into Suzhou numerals. Japanese continued to use the traditional forms. Examples: In Japan, Seki Takakazu developed the rod num