|
Al-Karaji
( fa, ابو بکر محمد بن الحسن الکرجی; c. 953 – c. 1029) was a 10th-century Persian people, Persian mathematician and engineer who flourished at Baghdad. He was born in Karaj, a city near Tehran. His three principal surviving works are mathematical: ''Al-Badi' fi'l-hisab'' (''Wonderful on calculation''), ''Al-Fakhri fi'l-jabr wa'l-muqabala'' (''Glorious on algebra''), and ''Al-Kafi fi'l-hisab'' (''Sufficient on calculation''). Work Al-Karaji wrote on mathematics and engineering. Some consider him to be merely reworking the ideas of others (he was influenced by Diophantus) but most regard him as more original, in particular for the beginnings of freeing algebra from geometry. Among historians, his most widely studied work is his algebra book ''al-fakhri fi al-jabr wa al-muqabala'', which survives from the medieval era in at least four copies. In his book "Extraction of hidden waters" he has mentioned that earth is spherical in shape but considers it t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics In Medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius of Perga, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry. Arabic works played an important role in the transmission of mathematics to Europe during the 10th—12th centuries. Concepts Algebra The study of algebra, the name of which is derived from the Arabic language, Arabic word meaning completion or "reunion of broken parts", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a Persian scholar in the House of Wisdom in Baghdad was the founder of algebra, is along with the Greek people, Greek mathematician Diophantus, known as the father of algebra. In his book ''The Compendious Book on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ibn Yahyā Al-Maghribī Al-Samaw'al
Al-Samawʾal ibn Yaḥyā al-Maghribī ( ar, السموأل بن يحيى المغربي, ; c. 1130 – c. 1180), commonly known as Samau'al al-Maghribi, was a mathematician, astronomer and physician. Born to a Jewish family, he concealed his conversion to Islam for many years in fear of offending his father, then openly embraced Islam in 1163 after he had a dream telling him to do so. His father was a Rabbi from Morocco. Mathematics Al-Samaw'al wrote the mathematical treatise ''al-Bahir fi'l-jabr'', meaning "The brilliant in algebra", at the age of nineteen. He also used the two basic concepts of mathematical induction, though without stating them explicitly. He used this to extend results for the binomial theorem up to n=12 and Pascal's triangle previously given by al-Karaji. Polemics He also wrote a famous polemic book in Arabic debating Judaism known as ''Ifḥām al-Yahūd'' (''Confutation of the Jews''). A Latin tract translated from Arabic and later translated into many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abū Kāmil Shujāʿ Ibn Aslam
Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ ( Latinized as Auoquamel, ar, أبو كامل شجاع بن أسلم بن محمد بن شجاع, also known as ''Al-ḥāsib al-miṣrī''—lit. "the Egyptian reckoner") (c. 850 – c. 930) was a prominent Egyptian mathematician during the Islamic Golden Age. He is considered the first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations. His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important part in introducing algebra to Europe. Abu Kamil made important contributions to algebra and geometry. He was the first Islamic mathematician to work easily with algebraic equations with powers higher than x^2 (up to x^8), and solved sets of non-linear simultaneous equations with three unknown variables. He illustrated the rules of signs for expanding the multiplication (a \pm b)(c \pm d). He wrote all problems rhetorically, and s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Iranian Scientists
The following is a non-comprehensive list of Iranian scientists, engineers, and scholars who lived from antiquity up until the beginning of the modern age. For the modern era, see List of contemporary Iranian scientists, scholars, and engineers. For mathematicians of any era, see List of Iranian mathematicians. (A person may appear on two lists, e.g. Abū Ja'far al-Khāzin.) A * Abdul Qadir Gilani (12th century) theologian and philosopher * Abu al-Qasim Muqane'i (10th century) physician * Abu Dawood (c. 817–889), Islamic scholar * Abu Hanifa (699–767), Islamic scholar * Abu Said Gorgani (10th century) * 'Adud al-Dawla (936–983), scientific patron * Ahmad ibn Farrokh (12th century), physician * Ahmad ibn 'Imad al-Din (11th century), physician and chemist * Alavi Shirazi (1670–1747), royal physician to Mughal Empire of South Asia * Amuli, Muhammad ibn Mahmud (c. 1300–1352), physician * Abū Ja'far al-Khāzin (900–971), mathematician and astronomer * Ansari, K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karaj
Karaj ( fa, کرج, ) is the capital of Alborz Province, Iran, and effectively a satellite city of Tehran. Although the county hosts a population around 1.97 million, as recorded in the 2016 census, most of the county is rugged mountain. The urban area is the fourth-largest in Iran, after Tehran, Mashhad, and Isfahan. Eshtehard County and Fardis County were split off from Karaj County since the previous census. The earliest records of Karaj date back to the 30th century BC. The city was developed under the rule of the Safavid and Qajar dynasties and is home to historical buildings and memorials from those eras. This city has a unique climate due to access to natural resources such as many trees, rivers, and green plains. After Tehran, Karaj is the largest immigrant-friendly city in Iran, so it has been nicknamed "Little Iran." History The area around Karaj has been inhabited for thousands of years, such as at the Bronze Age site of Tepe Khurvin and the Iron Age site of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. Etymology The word ''polynomial'' join ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1029 Deaths
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
950s Births
95 or 95th may refer to: * 95 (number) * one of the years 95 BC, AD 95, 1995, 2095, etc. * 95th Division (other) * 95th Regiment ** 95th Regiment of Foot (other) * 95th Squadron (other) * Atomic number 95: americium *Microsoft Office 95 * Saab 95 * Windows 95 See also * 9 to 5 (other) 9 to 5, or working time, is the standard period of working hours for some employees. 9 to 5 or Nine to Five may also refer to: Film and television * ''9 to 5'' (film), a 1980 American comedy film ** ''9 to 5'' (soundtrack) * ''9 to 5'' (TV ser ... * * List of highways numbered {{Numberdis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mariusz Wodzicki
Mariusz Wodzicki (Count Wodzicki) (born 1956) is a Polish mathematician and nobleman, whose works primarily focus on analysis, algebraic k-theory, noncommutative geometry, and algebraic geometry. Wodzicki was born in Bytom, Poland in 1956. He received a MSc from Moscow State University in 1980, and he completed his doctoral degree in 1984 at the Steklov Institute of Mathematics in Moscow under the advisement of Yuri Manin (Spectral Asymmetry and Zeta-Functions). In 1985–1986 he was a research assistant at the Mathematical Institute, University of Oxford, after which he became an assistant professor at the Mathematical Institute of the Polish Academy of Sciences. He is currently a professor of mathematics at the University of California, Berkeley. In 1992, Wodzicki was an invited speaker of the European Congress of Mathematics in Paris (Algebraic K-theory and functional analysis). In 1994, he was an invited speaker of the International Congress of Mathematicians in Zürich (The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science In Medieval Islam
Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and beyond, spanning the period roughly between 786 and 1258. Islamic scientific achievements encompassed a wide range of subject areas, especially astronomy, mathematics, and medicine. Other subjects of scientific inquiry included alchemy and chemistry, botany and agronomy, geography and cartography, ophthalmology, pharmacology, physics, and zoology. Medieval Islamic science had practical purposes as well as the goal of understanding. For example, astronomy was useful for determining the ''Qibla'', the direction in which to pray, botany had practical application in agriculture, as in the works of Ibn Bassal and Ibn al-'Awwam, and geography enabled Abu Zayd al-Balkhi to make accurate maps. Islamic mathematicians such as Al-Khwarizmi, Av ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squared Triangular Number
In number theory, the sum of the first cubes is the square of the th triangular number. That is, :1^3+2^3+3^3+\cdots+n^3 = \left(1+2+3+\cdots+n\right)^2. The same equation may be written more compactly using the mathematical notation for summation: :\sum_^n k^3 = \bigg(\sum_^n k\bigg)^2. This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE). History Nicomachus, at the end of Chapter 20 of his ''Introduction to Arithmetic'', pointed out that if one writes a list of the odd numbers, the first is the cube of 1, the sum of the next two is the cube of 2, the sum of the next three is the cube of 3, and so on. He does not go further than this, but from this it follows that the sum of the first cubes equals the sum of the first n(n+1)/2 odd numbers, that is, the odd numbers from 1 to n(n+1)-1. The average of these numbers is obviously n(n+1)/2, and there are n(n+1)/2 of them, so their sum is \bigl(n(n+1)/2\bigr)^2. Many early mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
