The Byzantines (Constantinople Fell to the Turcks ) stuck to the Greek numerical system, which represented numbers using various combinations of letters in the Greek alphabet. The scholar Maximos Planoudes (d. ca. 1305) wrote a treatise on what we call Arabic numerals, explaining how to use them in arithmetic and calling them “Indian” (which is technically correct). Here is how he introduced the system: Given that numbers are infinite, but we cannot have infinite numbers, the more philosophical astronomers invented signs and a method for using them so that they could precisely write the numbers they needed in a concise way. There are only nine of these signs: 1 2 3 4 5 6 7 8 9. They also postulate another sign that they call the cipher, which according to the Indians means “nothing.” All nine signs are Indian in origin; the cipher is written as 0 (Planoudes, The Great Method of Calculation according to the Indians 1).
The Arabic numbers made all the difference. It was heard in the streets of Constantinople just before the fall, that the men would rather wear an Islamic turban than a Roman Tiara
The word 'algorithm' has its roots in Latinizing the nisba, indicating his geographic origin, of the name of Persian mathematician Muhammad ibn Musa al-Khwarizmi to algorismus.[19][20] Al-Khwārizmī (Arabized Persian الخوارزمی c. 780–850) was a mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad,[13] whose name means 'the native of Khwarazm', a region that was part of Greater Iran and is now in Uzbekistan.[21][22] About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, which was translated into Latin during the 12th century. The manuscript starts with the phrase Dixit Algorizmi ('Thus spake Al-Khwarizmi'), where "Algorizmi" was the translator's Latinization of Al-Khwarizmi's name.[23] Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through another of his books, the Algebra.[24] In late medieval Latin, algorismus, English 'algorism', the corruption of his name, simply meant the "decimal number system".[25] In the 15th century, under the influence of the Greek word ἀριθμός (arithmos), 'number' (cf. 'arithmetic'), the Latin word was altered to algorithmus, and the corresponding English term 'algorithm' is first attested in the 17th century; the modern sense was introduced in the 19th century.[26]
In English, it was first used in about 1230 and then by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English.[27]
The word algorithm itself is derived from the name of the 9th-century mathematician Muḥammad ibn Mūsā al-Khwārizmī, whose nisba (identifying him as from Khwarazm) was Latinized as Algoritmi.[16] A partial formalization of the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as attempts to define "effective calculability"[17] or "effective method".[18] Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939.
https://en.wikipedia.org/wiki/Algorithm
https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system
The gradual development of the Hindu–Arabic numeral system independently devised the place-value concept and positional notation, which combined the simpler methods for computations with a decimal base, and the use of a digit representing 0. This allowed the system to consistently represent both large and small integers—an approach which eventually replaced all other systems. In the early 6th century AD, the Indian mathematician Aryabhata incorporated an existing version of this system in his work, and experimented with different notations. In the 7th century, Brahmagupta established the use of 0 as a separate number, and determined the results for multiplication, division, addition and subtraction of zero and all other numbers—except for the result of division by zero. His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, "Indians possess a method of calculation that no word can praise enough. Their rational system of mathematics, or of their method of calculation. I mean the system using nine symbols."[8] The Arabs also learned this new method and called it hesab.
Leobniz's Stepped Reckoner was the first calculator that could perform all four arithmetic operations.
Although the Codex Vigilanus described an early form of Arabic numerals (omitting 0) by 976 AD, Leonardo of Pisa (Fibonacci) was primarily responsible for spreading their use throughout Europe after the publication of his book Liber Abaci in 1202. He wrote, "The method of the Indians (Latin Modus Indorum) surpasses any known method to compute. It's a marvelous method. They do their computations using nine figures and symbol zero".[9]
In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities.
The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal notation.
Various types of tools have been invented and widely used to assist in numeric calculations. Before Renaissance, they were various types of abaci. More recent examples include slide rules, nomograms and mechanical calculators, such as Pascal's calculator. At present, they have been supplanted by electronic calculators and computers.
https://en.wikipedia.org/wiki/Arithmetic
The Hindu–Arabic numeral system or Indo-Arabic numeral system [1] (also called the Arabic numeral system or Hindu numeral system)[2][note 1] is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.
It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Persian Al-Khwārizmī[3] (On the Calculation with Hindu Numerals, c. 825) and Al-Kindi (On the Use of the Hindu Numerals, c. 830). The system later spread to medieval Europe by the High Middle Ages.
The system is based upon ten (originally nine) glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages.
These symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals used in the Middle East, and the Indian numerals in various scripts used in the Indian subcontinent.
see also
https://en.wikipedia.org/wiki/Cherokee_syllabary#Numerals
Cherokee generally uses Arabic numerals (0–9). In the late 1820s, several years after the introduction and adoption of his syllabary, Sequoyah proposed a set of number signs for Cherokee; however, these were never adopted and never typeset.[14] In 2012, the Cherokee Language Consortium agreed to begin using Sequoyah's numerals in some instances.[15]
Sequoyah developed unique characters for 1 through 19, and then characters for the "tens" of 20 through 100. Additional symbols were used to note thousands and millions, and Sequoyah also used a final symbol to mark the end of a number.[14][16] The glyphs for 1 through 20 can be grouped into groups of five that have a visual similarity to each other (1–5, 6–10, 11–15, and 16–20).[17] The Cherokee Language Consortium has created an additional symbol for zero along with symbols for billions and trillions.[15] As of Unicode 13.0, Cherokee numerals are not encoded within Unicode.[18]
Sequoyah's proposed numeral system has been described as having a "ciphered-additive structure,"[16] using combinations of the characters for 1 through 9 with the characters for 20 through 100 to create larger numbers. For example, instead of writing 64, the Cherokee numerals for 60 and 4 (Cherokee 64.svg) would be written together. To write 10 through 19, unique characters for each number are employed. For numbers larger than 100, the system takes on features of a multiplicative-additive system, with the digits for 1 through being placed before the 100 sign to indicate large numbers;[16] for example, for 504, the Cherokee numerals for 5, 100, and 4 (Cherokee 504.svg) would be written together.
Early historyAround 1809, impressed by the "talking leaves" of European written languages, Sequoyah began work to create a writing system for the Cherokee language. After attempting to create a character for each word, Sequoyah realized this would be too difficult and eventually created characters to represent syllables. He worked on the syllabary for twelve years before completion and dropped or modified most of the characters he originally created.
After the syllabary was completed in the early 1820s, it achieved almost instantaneous popularity and spread rapidly throughout Cherokee society.[20] By 1825, the majority of Cherokees could read and write in their newly developed orthography.[21]
No comments:
Post a Comment