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Lattice Multiplication
Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers. It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use. The method had already arisen by medieval times, and has been used for centuries in many different cultures. It is still being taught in certain curricula today. Method A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-dow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of ''Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in modern- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Napier's Bones
Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called ''rabdology'', a word invented by Napier. Napier published his version in 1617. It was printed in Edinburgh and dedicated to his patron Alexander Seton. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. Advanced use of the rods can extract square roots. Napier's bones are not the same as logarithms, with which Napier's name is also associated, but are based on dissected multiplication tables. The complete device usually includes a base board with a rim; the user places Napier's rods inside the rim to conduct multiplication or division. The board's left edge is divided into nine squares, holding the numbers 1 to 9. In Napier's original design, the rods are made of metal, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrakçı Nasuh
Nasuh bin Karagöz bin Abdullah el-Visokavi el-Bosnavî, commonly known as Matrakçı Nasuh (; ) for his competence in the combat sport of '' Matrak'' which was invented by himself, (also known as ''Nasuh el-Silâhî'', ''Nasuh the Swordsman'', because of his talent with weapons; 1480 – 1564) was a 16th-century Turk-Bosniak statesman of the Ottoman Empire, polymath, mathematician, teacher, historian, geographer, cartographer, swordmaster, navigator, inventor, painter, farmer, and miniaturist. He was brought to Istanbul after being recruited by Ottoman scouts in Rumelia. He was then educated, served several Ottoman sultans, and became a teacher at Enderun School. Life Matrakçı Nasuh, born in the Bosnian town of Visoko, was a Janissary who went through both the infantry and the devşirme system. He was a swordsman and sharpshooter who spoke five languages and was recruited into the Ottoman Navy. Although born to Bosnian Muslim parentage, Nasuh was drafted into the devş ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ottoman Bosnia
The Ottoman Empire era of rule in Bosnia and Herzegovina (first as a ''sanjak'', then as an ''eyalet'') and Herzegovina (also as a ''sanjak'', then ''eyalet'') lasted from 1463/1482 to 1878 ''de facto'', and until 1908 ''de jure''. Ottoman conquest The Ottoman conquest of Bosnia and Herzegovina started in 1384, and subsequently the Ottoman invasion expanded into the so-called Bosansko Krajište. The Kingdom of Bosnia finally fell in 1463. Herzegovina fell to the Turks in 1482. It took another century for the western parts of today's Bosnia to succumb to Ottoman attacks. Bosnia continued legally under the royal House of Berislavić, and fell finally in 1527 with the fall of its capital Jajce. The first occupation administration was established that same year. A significant number of Bosnians converted to Islam after the conquest by the Ottoman Empire in the second half of the 15th century, giving it a unique character within the Balkan region. This conversion appears t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhāskara II
Bhāskara II (c. 1114–1185), also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhāskara II to avoid confusion with Bhāskara I, was an Indian mathematician and astronomer. From verses, in his main work, Siddhānta Shiromani (सिद्धांतशिरोमणी), it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Sahyadri mountain ranges of Western Ghats, believed to be the town of Patan in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. He is the only ancient mathematician who has been immortalized on a monument. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the ban ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summa De Arithmetica
' (''Summary of arithmetic, geometry, proportions and proportionality'') is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work. Written in vernacular Italian, the ''Summa'' is the first printed work on algebra, and it contains the first published description of the double-entry bookkeeping system. It set a new standard for writing and argumentation about algebra, and its impact upon the subsequent development and standardization of professional accounting methods was so great that Pacioli is sometimes referred to as the "father of accounting". Contents The ''Summa de arithmetica'' as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Several of his works were plagiarised from Piero della Francesca, in what has been called "probably the first full-blown case of plagiarism in the history of mathematics". Life Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (''i.e.'', the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treviso Arithmetic
The ''Treviso Arithmetic'', or ''Arte dell'Abbaco'', is an anonymous textbook in commercial arithmetic written in vernacular Venetian language, Venetian and published in Treviso, Italy, in 1478. The author explains the motivation for writing this textbook: The ''Treviso Arithmetic'' is the earliest known printed mathematics book in the West, and one of the first printed European textbooks dealing with a science. The ''Arithmetic'' as an early printed book There appears to have been only one edition of the work. David Eugene Smith translated parts of the'' Treviso Arithmetic'' for educational purposes in 1907. Frank J. Swetz translated the complete work using Smith's notes in 1987 in his ''Capitalism & Arithmetic: The New Math of the 15th Century''. Swetz used a copy of the ''Treviso'' housed in the Manuscript Library at Columbia University. The volume found its way to this collection via a curious route. Maffeo Pinelli (1785), an Italian bibliophile, is the first known owner. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jamshīd Al-Kāshī
Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) ( fa, غیاث الدین جمشید کاشانی ''Ghiyās-ud-dīn Jamshīd Kāshānī'') (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician during the reign of Tamerlane. Much of al-Kāshī's work was not brought to Europe, and still, even the extant work, remains unpublished in any form. Biography Al-Kashi was born in 1380, in Kashan, in central Iran. This region was controlled by Tamerlane, better known as Timur. The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Turkish princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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