In the history of mathematics, Islamic mathematics refers to the mathematics developed in the Islamic world between 622 and 1600, in the part of the world where Islam was the dominant religious and cultural influence. The area of study known as the history of mathematics is primarily an investigation into the origin of new discoveries in Mathematics and to a lesser extent an investigation Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The term Muslim world (or Islamic world) has several meanings Events Religion July 16 — Year one of the Islamic calendar begins during which the Hijra occurs — Prophet Muhammad For other meanings including people named 'Islam' see Islam (disambiguation. Islamic science and mathematics flourished under the Islamic caliphate (also known as the Islamic Empire) established across the Middle East, Central Asia, North Africa, Sicily, the Iberian Peninsula, and in parts of France and India in the 8th century. The Caliph is the Head of state in a Caliphate, and the title for the leader of the Islamic Ummah, an Islamic community ruled by the Shari'ah The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. Central Asia is a region of Asia from the Caspian Sea in the west to central China in the east and from southern Russia in the north to northern Pakistan in the south North Africa or Northern Africa is the Northernmost Region of the African Continent, separated by the Sahara from Sub-Saharan Sicily ( Italian and Sicilian: Sicilia) is an autonomous region of Italy. The Iberian Peninsula, or Iberia, is located in the extreme southwest of Europe, and includes modern day Spain, Portugal, Andorra This article is about the country For a topic outline on this subject see List of basic France topics. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country The center of Islamic mathematics was located in present-day Iraq and Iran, but at its greatest extent stretched from Turkey, North Africa and Spain in the west, to India in the east. For a topic outline on this subject see List of basic Iraq topics. For a topic outline on this subject see List of basic Iran topics. Turkey (Türkiye known officially as the Republic of Turkey ( is a Eurasian Country that stretches North Africa or Northern Africa is the Northernmost Region of the African Continent, separated by the Sahara from Sub-Saharan Spain () or the Kingdom of Spain (Reino de España is a country located mostly in southwestern Europe on the Iberian Peninsula. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country ^[1]

While most scientists in this period were Muslims and Arabic was the dominant language—much like Latin in Medieval Europe, Arabic was used as the written language of scholars throughout the Islamic world at the time—contributions were made by people of different ethnic groups (Arabs, Moors, Persians, Turks) and religions (Muslims, Christians, Sabians, Jews, Zoroastrians). A Muslim (مسلم pronounced Muslim, not Muzlim) is an adherent of the Religion Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. The term Muslim world (or Islamic world) has several meanings The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding The description Moors has referred to several historic and modern populations of Muslim (and earlier non-Muslim people of Berber and Arab descent layout and formatting it should ensure no clashes with the top of the infobox The Turkic peoples are Eurasian peoples residing in northern central and western Eurasia who speak languages belonging to the Turkic language family A Muslim (مسلم pronounced Muslim, not Muzlim) is an adherent of the Religion A Christian is a person who adheres to Christianity, a monotheistic Religion centered on the life and teachings of Jesus of Nazareth Sabian is a Canadian Cymbal designer and manufacturer It is one of the largest in the world along with Zildjian, Paiste and Meinl. PLEASE TAKE NOTE************ Zoroastrianism (ˌzɔroʊˈæstriəˌnɪzəm is the religion and philosophy based on the teachings ^[2] In particular, a large number of Islamic scientists in many disciplines, including mathematics, were Persians. ^[3]

Origins and influences

The first century of the Islamic Arab Empire saw almost no scientific or mathematical achievements since the Arabs, with their newly conquered empire, had not yet gained any intellectual drive and research in other parts of the world had faded. For other meanings including people named 'Islam' see Islam (disambiguation. In the second half of the eighth century Islam had a cultural awakening, and research in mathematics and the sciences increased. ^[4] The Muslim Abbasid caliph al-Mamun (809-833) is said to have had a dream where Aristotle appeared to him, and as a consequence al-Mamun ordered that Arabic translation be made of as many Greek works as possible, including Ptolemy's Almagest and Euclid's Elements. The Caliph is the Head of state in a Caliphate, and the title for the leader of the Islamic Ummah, an Islamic community ruled by the Shari'ah Abu Jafar al-Ma'mun ibn Harun (also spelled Almamon and el-Mâmoûn) ( September 14, 786 &ndash August 9, 833) (المأمون Greek works would be given to the Muslims by the Byzantine Empire in exchange for treaties, as the two empires held an uneasy peace. ^[4] Many of these Greek works were translated by Thabit ibn Qurra (826-901), who translated books written by Euclid, Archimedes, Apollonius, Ptolemy, and Eutocius. (836 in Harran, Mesopotamia &ndash February 18, 901 in Baghdad) was an Arab astronomer, mathematician Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca ^[5] Historians are in debt to many Islamic translators, for it is through their work that many ancient Greek texts have survived only through Arabic translations. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language

Greek, Indian, and Mesopotamian mathematics all played an important role in the development of early Islamic mathematics. Greek mathematics, as that term is used in this article is the Mathematics written in Greek, developed from the 6th century BC to the 5th century Indian mathematics &mdashwhich here is the mathematics that emerged in South Asia zero, Negative numbers, Arithmetic, and Algebra. Mesopotamia (from the Greek meaning "land between the rivers" is an area geographically located between the Tigris and Euphrates rivers largely corresponding The works of mathematicians such as Euclid, Apollonius, Archimedes, Diophantus, Aryabhata and Brahmagupta were all acquired by the Islamic world and incorporated into their mathematics. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer Diophantus of Alexandria ( Greek: b between 200 and 214 d between 284 and 298 AD sometimes called "the father of Algebra " a title some claim should Āryabhaṭa ( Devanāgarī: आर्यभट (AD 476 &ndash 550 is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics Brahmagupta ( (598–668 was an Indian mathematician and astronomer. Perhaps the most influential mathematical contribution from India was the decimal place-value Indo-Arabic numeral system, also known as the Hindu numerals. India, officially the Republic of India (भारत गणराज्य inc-Latn Bhārat Gaṇarājya; see also other Indian languages) is a country A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century The Hindu-Arabic numeral system is a Positional Decimal Numeral system first documented in the ninth century ^[6] The Persian historian al-Biruni (c. layout and formatting it should ensure no clashes with the top of the infobox 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India from which was brought a book to Baghdad that was translated into Arabic as Sindhind. The Caliph is the Head of state in a Caliphate, and the title for the leader of the Islamic Ummah, an Islamic community ruled by the Shari'ah Abu Jafar al-Ma'mun ibn Harun (also spelled Almamon and el-Mâmoûn) ( September 14, 786 &ndash August 9, 833) (المأمون It is generally assumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta. The main work of Brahmagupta, Brahmasphuta-siddhanta (The Opening of the Universe, written in the year 628, contains some remarkably advanced ideas including ^[7] The earliest translations from Sanskrit inspired several astronomical and astrological Arabic works, now mostly lost, some of which were even composed in verse. ^[8]

But Indian influences were soon overwhelmed by Greek mathematical and astronomical texts. It is not clear why this occurred but it may have been due to the greater availability of Greek texts in the region, the larger number of practitioners of Greek mathematics in the region, or because Islamic mathematicians favored the deductive exposition of the Greeks over the elliptic Sanskrit verse of the Indians. Regardless of the reason, Indian mathematics soon became mostly eclipsed by or merged with the "Graeco-Islamic" science founded on Hellenistic treatises. ^[8]

Importance

J. J. O'Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

"Recent research paints a new picture of the debt that we owe to Islamic mathematics. The MacTutor History of Mathematics archive is an award-winning website maintained by John J Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the 16th, 17th, and 18th centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects, the mathematics studied today is far closer in style to that of Islamic mathematics than to that of Greek mathematics. Greek mathematics, as that term is used in this article is the Mathematics written in Greek, developed from the 6th century BC to the 5th century "

R. Rashed wrote in The development of Arabic mathematics: between arithmetic and algebra:

"Al-Khwarizmi's successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose. In Mathematics, the symmetric algebra S ( V) (also denoted Sym ( V) on a Vector space V over a field Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics) An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent "

Biographies

Al-Ḥajjāj ibn Yūsuf ibn Maṭar (786 – 833)

Al-Ḥajjāj translated Euclid's Elements into Arabic. (786–833 was an Arab Mathematician who made the first translation of Euclid 's Elements from Greek into Arabic Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek

Muḥammad ibn Mūsā al-Khwārizmī (c. 780 Khwarezm/Baghdad – c. Khwarezm were a series of States centered on the Amu Darya River delta of the Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous 850 Baghdad)

Al-Khwārizmī was a Persian mathematician, astronomer, astrologer and geographer. A mathematician is a person whose primary area of study and research is the field of Mathematics. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Astrology (from Greek grc ἄστρον astron, "constellation star" and grc -λογία -logia) is a group of Systems A geographer is a Scientist whose area of study is Geography, the study of Earth 's physical environment and Human habitat He worked most of his life as a scholar in the House of Wisdom in Baghdad. Scholarly method &mdash or as it is more commonly called scholarship &mdash is the body of principles and practices used by scholars to make their claims about the world as The House of Wisdom ( Arabic: بيت الحكمة; Bait al-Hikma) was a library and translation institute in Abbassid -era Baghdad, Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous His Algebra was the first book on the systematic solution of linear and quadratic equations. A linear equation is an Algebraic equation in which each term is either a Constant or the product of a constant and (the first power of a single Variable In Mathematics, a quadratic equation is a Polynomial Equation of the second degree. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the 12th century. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Most of the positional Base 10 Numeral systems in the world have originated from India, which first developed the concept of positional numerology The decimal ( base ten or occasionally denary) Numeral system has ten as its base. A positional notation or place-value notation system is a Numeral system in which each position is related to the next by a Constant multiplier a The term Western world, the West or the Occident ( Latin: occidens -sunset -west as distinct from the Orient) can have multiple meanings He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology. Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca

Al-ʿAbbās ibn Saʿid al-Jawharī (c. (c 800 Baghdad? &ndash c 860 Baghdad? was a Geometer who worked at the House of Wisdom in Baghdad and for in a short time in Damascus where 800 Baghdad? – c. 860 Baghdad?)

Al-Jawharī was a mathematician who worked at the House of Wisdom in Baghdad. His most important work was his Commentary on Euclid's Elements which contained nearly 50 additional propositions and an attempted proof of the parallel postulate. Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive

ʿAbd al-Hamīd ibn Turk (fl. ( Turkey / Iraq ? fl 830 was a Ninth century Muslim mathematician. 830 Baghdad)

Ibn Turk wrote a work on algebra of which only a chapter on the solution of quadratic equations has survived. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. In Mathematics, a quadratic equation is a Polynomial Equation of the second degree.

Yaʿqūb ibn Isḥāq al-Kindī (c. ( أبو يوسف يعقوب إبن إسحاق الكندي) (c 801 Kufah – 873 Baghdad)

Al-Kindī (or Alkindus) was a philosopher and scientist who worked as the House of Wisdom in Baghdad where he wrote commentaries on many Greek works. Kufa ( Arabic, ar الكوفة) is a city in modern Iraq, about 170 km south of Baghdad, and 10 km northeast of Najaf. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language A scientist, in the broadest sense refers to any person that engages in a systematic activity to acquire Knowledge or an individual that engages in such practices His contributions to mathematics include many works on arithmetic and geometry. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position

Hunayn ibn Ishaq (808 Al-Hirah – 873 Baghdad)

Hunayn (or Johannitus) was a translator who worked at the House of Wisdom in Baghdad. Hunayn ibn Ishaq (Hunein Bit Ishak أبو زيد حنين بن إسحاق العبادي; known in Latin as Johannitius (809-873 was a famous and influential Al Hīra ( Arabic, الحيرة) was an ancient city located south of Al-Kufah in south-central Iraq. Translated many Greek works including those by Plato, Aristotle, Galen, Hippocrates, and the Neoplatonists. Biography Early life Birth and family Plato was born in Athens Greece Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Galen ( Greek: Γαληνός Galēnos; Latin: Claudius Galenus, Aelius Galenus, Claudius Aelius Galenus, or Hippocrates of Cos II or Hippokrates of Kos ( ca. 460 BC – ca Neoplatonism (also Neo-Platonism) is the modern term for a school of religious and mystical Philosophy that took shape in the 3rd century AD founded by

Banū Mūsā (c. The Banū Mūsā brothers (بنو موسى "Sons of Mūsā" were three 9th century Persian Scholars of Baghdad, active in the House 800 Baghdad – 873+ Baghdad)

The Banū Mūsā where three brothers who worked at the House of Wisdom in Baghdad. Their most famous mathematical treatise is The Book of the Measurement of Plane and Spherical Figures, which considered similar problems as Archimedes did in his On the measurement of the circle and On the sphere and the cylinder. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer They contributed individually as well. The eldest, Jaʿfar Muḥammad (c. 800) specialised in geometry and astronomy. He wrote a critical revision on Apollonius' Conics called Premises of the book of conics. Aḥmad (c. The Banū Mūsā brothers (بنو موسى "Sons of Mūsā" were three 9th century Persian Scholars of Baghdad, active in the House 805) specialised in mechanics and wrote a work on pneumatic devices called On mechanics. Pneumatics, Pressurized gas to affect mechanical motion Pneumatic power is used in Industry, where it is common to have factory units plumbed for Compressed The youngest, al-Ḥasan (c. The Banū Mūsā brothers (بنو موسى "Sons of Mūsā" were three 9th century Persian Scholars of Baghdad, active in the House 810) specialised in geometry and wrote a work on the ellipse called The elongated circular figure. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a

Al-Mahani

Ahmed ibn Yusuf

Thabit ibn Qurra (Syria-Iraq, 835-901)

Al-Hashimi (Iraq? ca. Abu-Abdullah Muhammad ibn Īsa Māhānī, was a Persian mathematician and astronomer from Mahan, Kerman, Persia. Ahmed ibn Yusuf ibn Ibrahim ibn Tammam al-siddiq Al-Baghdadi also known as Abu Ja'far Ahmad ibn Yusuf and Ahmed ibn Yusuf al-misri (835 - 912 was an Arab (836 in Harran, Mesopotamia &ndash February 18, 901 in Baghdad) was an Arab astronomer, mathematician 850-900)

Muḥammad ibn Jābir al-Ḥarrānī al-Battānī (c. 853 Harran – 929 Qasr al-Jiss near Samarra)

Abu Kamil (Egypt? ca. Sāmarrā ( Arabic, سامَرّاء) is a city in Iraq. It stands on the east bank of the Tigris (c 850 – c 930 (ابو كامل for short was an Egyptian Muslim mathematician during the Islamic Golden Age. 900)

Sinan ibn Tabit (ca. Sinan ibn Thabit ibn Qurra ( Arabic, سنان بن ثابت بن قرة) was an Arab physician, mathematician and astronomer 880 - 943)

Al-Nayrizi

Ibrahim ibn Sinan (Iraq, 909-946)

Al-Khazin (Iraq-Iran, ca. Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī ( ar أبو العباس الفضل بن حاتم النيريزي Latin name Anaritius) was a 9th-10th Ibrahim ibn Sinan ibn Thabit ibn Qurra (908 Baghdad – 946 Baghdad was an Arab Mathematician and Astronomer who studied Geometry Abu Jafar Muhammad ibn al-Hasan Al-Khazini (900-971 was a Persian astronomer and mathematician from Khorasan. 920-980)

Al-Karabisi (Iraq? 10th century?)

Ikhwan al-Safa' (Iraq, first half of 10th century)

The Ikhwan al-Safa' ("brethren of purity") were a (mystical?) group in the city of Basra in Irak. The Brethren of Purity ( Arabic اخوان الصفا Ikhwan al-Safa; also translated as Brethren of Sincerity) were a mysterious The group authored a series of more than 50 letters on science, philosophy and theology. The first letter is on arithmetic and number theory, the second letter on geometry.

Al-Uqlidisi (Iraq-Iran, 10th century)

Al-Saghani (Iraq-Iran, ca. Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab Mathematician, possibly from Damascus. Abu Hamid Ahmed ibn Mohammed al-Saghani al-Asturlabi (meaning the Astrolabe maker of Saghan near Merv) was a Persian astronomer and historian of science 940-1000)

Abū Sahl al-Qūhī (Iraq-Iran, ca. (sometimes) was a Persian mathematician, physicist and astronomer. 940-1000)

Al-Khujandi

Abū al-Wafāʾ al-Būzjānī (Iraq-Iran, ca. Abu Mahmood Khujandi or Abu Mahmud Hamid ibn al-Khidr Al-Khujandi (Persian ابومحمود خجندی was a Persian ( Tajik) astronomer and 940-998)

Ibn Sahl (Iraq-Iran, ca. This article is about the physicist For the physician see Ali ibn Sahl Rabban al-Tabari. 940-1000)

Al-Sijzi (Iran, ca. Abu Sa'id Ahmed ibn Mohammed ibn Abd al-Jalil al-Sijzi (short for al-Sijistani was a Persian astronomer and mathematician. 940-1000)

Labana of Cordoba (Spain, ca. 10th century)

One of the few Islamic female mathematicians known by name, and the secretary of the Umayyad Caliph al-Hakem II. The Caliphate of Córdoba (Arabic خلافة قرطبة ruled the Iberian peninsula ( Al-Andalus) and North Africa from the city of She was well-versed in the exact sciences, and could solve the most complex geometrical and algebraic problems known in her time. ^[9]

Ibn Yunus (Egypt, ca. Ibn Yunus ( Arabic: ابن يونس) (full name Abu al-Hasan 'Ali abi Sa'id 'Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi al-Misri (c 950-1010)

Abu Nasr ibn `Iraq (Iraq-Iran, ca. Abu Nasr Mansur ibn Ali ibn Iraq (c 960 - 1036 was a was a Persian Muslim mathematician. 950-1030)

Kushyar ibn Labban (Iran, ca. Abul-Hasan Kūshyār ibn Labbān ibn Bashahri Gilani (971 - 1029 also known as Kūshyār Gīlānī ( was a Persian mathematician geographer and astronomer from Jilan 960-1010)

Al-Karaji (Iran, ca. (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. 970-1030)

Ibn al-Haytham (Iraq-Egypt, ca. TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized 965-1040)

Abū al-Rayḥān al-Bīrūnī (September 15, 973 in Kath, Khwarezm – December 13, 1048 in Gazna)

Ibn Sina

al-Baghdadi

Al-Nasawi

Al-Jayyani (Spain, ca. Events 668 - Eastern Roman Emperor Constans II is assassinated in his bath at Syracuse Italy. Events By Place Africa The Fatimids move their capital to Cairo. Khwarezm were a series of States centered on the Amu Darya River delta of the Events 1294 - Saint Celestine V abdicates the papacy after only five months Celestine hoped to return to his previous life Ghazni City ( - Ğaznī; Ghazna and Ghaznīn are the old names for Ghazni TemplateInfobox Muslim scholars --> ( Persian /ابو علی الحسین ابن عبدالله ابن سینا (born Abu Mansur Abd al-Qahir ibn Tahir ibn Muhammad ibn Abdallah al-Tamimi al-Shaffi al-Baghdadi ( Arabic:أبو منصور عبدالقاهر ابن طاهر بن محمد بن عبدالله (c 1010 possibly in Nasa, Khurasan &ndash c 1075 in Baghdad) was a Persian mathematician from Khurasan, Iran. Abu Abd Allah Muhammad ibn Muadh Al-Jayyani, shortened to Al-Jayyani ( 989, Cordova, Al-Andalus – 1079, Jaen, Al-Andalus 1030-1090)

Ibn al-Zarqalluh (Azarquiel, al-Zarqali) (Spain, ca. 1030-1090)

Al-Mu'taman ibn Hud (Spain, ca. Yusuf ibn Ahmad al-Mu'taman ibn Hud was an Arab Mathematician and a member of the Banu Hud family al-Mutamin ruled Zaragoza from 1082 1080)

al-Khayyam (Iran, ca. For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین 1050-1130)

Ibn Yaḥyā al-Maghribī al-Samawʾal (c. مغربي، السموءل بن يحي، also known as Samau'al al-Maghribi (c 1130 Baghdad – c. Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous 1180 Maragha)

Sharaf al-Dīn al-Ṭūsī (Iran, ca. (1135 - 1213 was a Persian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages) 1150-1215)

Ibn Mun`im (Maghreb, ca. 1210)

al-Marrakushi (Morocco, 13th century)

Naṣīr al-Dīn al-Ṭūsī (18 February 1201 in Tus, Khorasan – 26 June 1274 in Kadhimain near Baghdad)

Muḥyi al-Dīn al-Maghribī (c. Events 3102 BC - Epoch (origin of the Kali Yuga. 1229 - The Sixth Crusade: Frederick II Holy Toos (توس or طوس in Persian) also known as Tous or Tus, is an ancient city in the Iranian province of Razavi Khorasan Events 363 - Roman Emperor Julian is killed during the retreat from the Sassanid Empire. al-Kāżimiyyah (الكاظمية al-Kāżimiyyah; alternatively الكاظمين al-Kāżimayn) is a town located in what is now a northern neighbourhood of Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous ( Arabic,محي الدين المغربي (c1220 Spain &ndash c 1220 Spain – c. 1283 Maragha)

Shams al-Dīn al-Samarqandī (c. (c 1250 &ndash c 1310 was a 13th century astronomer and mathematician from Samarkand. 1250 Samarqand – c. Samarkand (Samarqand Самарқанд سمرقند UniPers: "Samarqand" is the second-largest city in Uzbekistan and the capital of 1310)

Ibn Baso (Spain, ca. 1250-1320)

Ibn al-Banna' (Maghreb, ca. 1300)

Kamal al-Din Al-Farisi (Iran, ca. Kamal al-Din Abu'l-Hasan Muhammad Al-Farisi (1267-ca1319/1320 (كمال‌الدين ابوالحسن محمد فارسی was a prominent Persian Muslim physicist 1300)

Al-Khalili (Syria, ca. (1320 - 1380 was an Arab Astronomer of Syria who compiled extensive tables for astronomical use 1350-1400)

Ibn al-Shatir (1306-1375)

Qāḍī Zāda al-Rūmī (1364 Bursa – 1436 Samarkand)

Jamshīd al-Kāshī (Iran, Uzbekistan, ca. Ala Al-Din Abu'l-Hasan Ali Ibn Ibrahim Ibn al-Shatir (1304 &ndash 1375 (ابن الشاطر was an Arab Muslim astronomer, mathematician, engineer Bursa (historically also known as Prussa, Greek: Προύσα and later as Brusa) is a city in northwestern Turkey and the seat (or, Persian: غیاث‌الدین جمشید کاشانی (c 1420)

Ulugh Beg (Iran, Uzbekistan, 1394-1449)

Al-Umawi

Abū al-Hasan ibn Alī al-Qalasādī (Maghreb, 1412-1482)

Later major medieval Arab mathematician. Ulugh Beg ( Chaghatay / - also Uluğ Bey, Ulugh Bek and Ulug Bek) (c Abū al-Hasan ibn ʿAlī al-Qalaṣādī (1412 in Baza, Spain &ndash 1486 in Béja, Tunisia) was an Arab Muslim mathematician The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding Pioneer of symbolic algebra

Fields

Algebra

See also: History of algebra

A page from The Compendious Book on Calculation by Completion and Balancing. See also Table of mathematical symbols Mathematical notation is used in Mathematics, and throughout the Physical sciences, Engineering Elementary algebra is the branch of Mathematics that deals with solving for the Operands of Arithmetic Equations. Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala ( Arabic for "The Compendious Book on Calculation by Completion and Balancing"

There are three theories about the origins of Arabic Algebra. The first emphasizes Hindu influence, the second emphasizes Mesopotamian or Persian-Syriac influence and the third emphasizes Greek influence. Many scholars believe that it is the result of a combination of all three sources. ^[10]

Throughout their time in power, before the fall of Islamic civilization, the Arabs used a fully rhetorical algebra, where sometimes even the numbers were spelled out in words. The Arabs would eventually replace spelled out numbers (eg. twenty-two) with Arabic numerals (eg. The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system 22), but the Arabs never adopted or developed a syncopated or symbolic algebra. ^[5]

The Muslim^[11] Persian mathematician Muhammad ibn Mūsā al-khwārizmī was a faculty member of the "House of Wisdom" (Bait al-hikma) in Baghdad, which was established by Al-Mamun. Al-Khwarizmi, who died around 850 A. D. , wrote more than half a dozen mathematical and astronomical works; some of which were based on the Indian Sindhind. ^[4] One of al-Khwarizmi's most famous books is entitled Al-jabr wa'l muqabalah or The Compendious Book on Calculation by Completion and Balancing, and it gives an exhaustive account of solving polynomials up to the second degree. Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala ( Arabic for "The Compendious Book on Calculation by Completion and Balancing" ^[12]

Al-Jabr is divided into six chapters, each of which deals with a different type of formula. The first chapter of Al-Jabr deals with equations whose squares equal its roots (ax² = bx), the second chapter deals with squares equal to number (ax² = c), the third chapter deals with roots equal to a number (bx = c), the fourth chapter deals with squares and roots equal a number (ax² + bx = c), the fifth chapter deals with squares and number equal roots (ax² + c = bx), and the sixth and final chapter deals with roots and number equal to squares (bx + c = ax²). ^[13]

'Abd al-Hamid ibn-Turk authored a manuscript entitled Logical Necessities in Mixed Equations, which is very similar to al-Khwarzimi's Al-Jabr and was published at around the same time as, or even possibly earlier than, Al-Jabr. ^[14] The manuscript gives the exact same geometric demonstration as is found in Al-Jabr, and in one case the same example as found in Al-Jabr, and even goes beyond Al-Jabr by giving a geometric proof that if the determinant is negative then the quadratic equation has no solution. ^[14] The similarity between these two works has led some historians to conclude that Arabic algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid. ^[14]

Al-Karkhi was the successor of Abu'l-Wefa and he was the first to discover the solution to equations of the form ax²ⁿ + bxⁿ = c. (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. ^[15] Al-Karkhi only considered positive roots. ^[15]

Omar Khayyám (c. 1050-1123) wrote a book on Algebra that went beyond Al-Jabr to include equations of the third degree. ^[16] Omar Khayyám provided both arithmetic and geometric solutions for quadratic equations, but he only gave geometric solutions for general cubic equations since he mistakenly believed that arithmetic solutions were impossible. ^[16] His method of solving cubic equations by using intersecting conics had been used by Menaechmus, Archimedes, and Alhazen, but Omar Khayyám generalized the method to cover all cubic equations with positive roots. ^[16] He only considered positive roots and he did not go past the third degree. ^[16] He also saw a strong relationship between Geometry and Algebra. ^[16]

In the 12th century, Sharaf al-Din al-Tusi found algebraic and numerical solutions to cubic equations and was the first to discover the derivative of cubic polynomials. (1135 - 1213 was a Persian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages) Numerical analysis is the study of Algorithms for the problems of continuous mathematics (as distinguished from Discrete mathematics) In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. ^[17]

J. J. O'Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

"Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. The MacTutor History of Mathematics archive is an award-winning website maintained by John J It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc. In Mathematics, a rational number is a number which can be expressed as a Ratio of two Integers Non-integer rational numbers (commonly called fractions In Mathematics, an irrational number is any Real number that is not a Rational number — that is it is a number which cannot be expressed as a fraction , to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. "

Abū al-Hasan ibn Alī al-Qalasādī (1412-1482) was the last major medieval Arab algebraist, who made the first attempt at creating an algebraic notation since Ibn al-Banna two centuries earlier, who was himself the first to make such an attempt since Diophantus and Brahmagupta in ancient times. Abū al-Hasan ibn ʿAlī al-Qalaṣādī (1412 in Baza, Spain &ndash 1486 in Béja, Tunisia) was an Arab Muslim mathematician The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding See also Table of mathematical symbols Mathematical notation is used in Mathematics, and throughout the Physical sciences, Engineering Diophantus of Alexandria ( Greek: b between 200 and 214 d between 284 and 298 AD sometimes called "the father of Algebra " a title some claim should Brahmagupta ( (598–668 was an Indian mathematician and astronomer. ^[18] The syncopated notations of his predecessors, however, lacked symbols for mathematical operations. In its simplest meaning in Mathematics and Logic, an operation is an action or procedure which produces a new value from one or more input values ^[19] Al-Qalasadi's algebraic notation was the first to have symbols for these functions and was thus "the first steps toward the introduction of algebraic symbolism. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. " He represented mathematical symbols using characters from the Arabic alphabet. This is a listing of common symbols found within all branches of the science of Mathematics. The Arabic alphabet is the script used for writing several languages of Asia and Africa such as Arabic, Persian, and Urdu. ^[18]

Arithmetic

Main article: Arabic numerals

The Indian numeral system came to be known to both the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals written circa 825, and the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Indian Numerals (Ketab fi Isti'mal al-'Adad al-Hindi) circa 830, are principally responsible for the diffusion of the Indian system of numeration in the Middle-East and the West [2]. The arabic numerals (often capitalized are the ten Digits (0 1 2 3 4 5 6 7 8 9 which—along with the system Most of the positional Base 10 Numeral systems in the world have originated from India, which first developed the concept of positional numerology layout and formatting it should ensure no clashes with the top of the infobox Events By Place Europe Egbert of Wessex defeats Beornwulf of Mercia at Ellandun. The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding ( أبو يوسف يعقوب إبن إسحاق الكندي) (c Events By Place Europe Earliest date of composition for the Historia Brittonum, attributed to Nennius, and known for The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions using decimal point notation, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952-953. The Middle East is a Subcontinent with no clear boundaries often used as a synonym to Near East, in opposition to Far East. In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object In a positional Numeral system, the decimal separator is a Symbol used to mark the boundary between the integral and the fractional Syrians today are an overall indigenous Levantine people closely related to their immediate neighbours like the Lebanese and (to a lesser extent Jordanians Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab Mathematician, possibly from Damascus. Events By Topic Asia Kalbid forces defeat the Byzantines in Calabria. Events Europe First documented mention of the village of Aach in Rhineland-Palatinate, Germany.

In the Arab world—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used the Abjad numerals. Babylonian numerals were written in cuneiform, using a wedge-tipped reed Stylus to make a mark on a soft Clay tablet which would be exposed The Abjad numerals are a decimal Numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values A distinctive "West Arabic" variant of the symbols begins to emerge in ca. the 10th century in the Maghreb and Al-Andalus, called the ghubar ("sand-table" or "dust-table") numerals. The Maghreb (المغرب العربي al-Maġrib al-ʿArabī) also rendered Maghrib (or rarely Moghreb) meaning "place of Sunset Al-Andalus (الأندلس was the Arabic name given to those parts of the Iberian Peninsula governed by Muslims or

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976 [3]. The Codex Vigilanus (Albeldensis or Códice Albeldense (Vigilano, full name Codex Conciliorum Albeldensis seu Vigilanus, is an illuminated For the 976 telephone prefix see Premium-rate telephone number Events By Place Byzantine Empire January 10 — From the 980s, Gerbert of Aurillac (later, Pope Silvester II) began to spread knowledge of the numerals in Europe. Events and Trends 983 — Pagan West Slavs revolt temporarily ending attempts at conversion and forcing abandonment of German sees and monasteries east Pope Sylvester II, or Silvester II (c 946&ndash May 12, 1003) born Gerbert d'Aurillac, was a prolific scholar teacher and Pope Pope Sylvester II, or Silvester II (c 946&ndash May 12, 1003) born Gerbert d'Aurillac, was a prolific scholar teacher and Pope Gerbert studied in Barcelona in his youth, and he is known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France. Barcelona ( Catalan bəɾsəˈlonə Spanish baɾθeˈlona is the capital and most populous city of the Autonomous Community of Catalonia The astrolabe is a historical Astronomical instrument used by classical astronomers, Navigators Lupitus of Barcelona, identified with a Christian Archdeacon called Sunifred, was an Astronomer in late 10th century Barcelona, then

Al-Khwārizmī, the Persian scientist, wrote in 825 a treatise On the Calculation with Hindu Numerals, which was translated into Latin in the 12th century, as Algoritmi de numero Indorum, where "Algoritmi", the translator's rendition of the author's name gave rise to the word algorithm (Latin algorithmus) with a meaning "calculation method". layout and formatting it should ensure no clashes with the top of the infobox Events By Place Europe Egbert of Wessex defeats Beornwulf of Mercia at Ellandun. The Renaissance of the 12th century saw a major search by European scholars for new learning which led them to the Arabic fringes of Europe especially to Islamic In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation

Calculus

Around 1000 AD, Al-Karaji, using mathematical induction, found a proof for the sum of integral cubes. (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. Mathematical induction is a method of Mathematical proof typically used to establish that a given statement is true of all Natural numbers It is done by proving that In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Arithmetic and Algebra, the cube of a number n is its third power &mdash the result of multiplying it by itself three times ^[20] The historian of mathematics, F. See also History An historian is an individual who studies and writes about History, and is regarded as an Authority on it Woepcke,^[21] praised Al-Karaji for being "the first who introduced the theory of algebraic calculus. The word theory has many distinct meanings in different fields of Knowledge, depending on their methodologies and the context of discussion. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives " Shortly afterwards, Ibn al-Haytham (known as Alhazen in the West), an Iraqi mathematician working in Egypt, was the first mathematician to derive the formula for the sum of the fourth powers. TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized For a topic outline on this subject see List of basic Iraq topics. During the initial Islamic invasion in 639 AD, Egypt was ruled at first by governors acting in the name of the Righteous Caliphs, and then the Ummayad In Mathematics and elsewhere the adjective quartic means fourth order, such as the function x^4 In turn, he developed a method for determining the general formula for the sum of any integral powers, which was fundamental to the development of integral calculus. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space ^[22]

The eleventh century Persian mathematician Omar Khayyám saw a strong relationship between geometry and algebra, and was moving in the right direction when he helped to close the gap between numerical and geometric algebra^[16] with his geometric solution of the general cubic equations,^[23] but the decisive step in analytic geometry came later with Descartes. The Persian Empire was a series of Iranian empires that ruled over the Iranian plateau, the original Persian homeland and beyond in Western Asia For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry ^[16] In the 12th century, the Persian mathematician Sharaf al-Din al-Tusi was the first to discover the derivative of cubic polynomials, an important result in differential calculus. layout and formatting it should ensure no clashes with the top of the infobox (1135 - 1213 was a Persian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages) In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. In mathematics and more specifically in Differential calculus, the term differential has several interrelated meanings ^[17]

Cryptography

In the 9th century, al-Kindi was a pioneer in cryptanalysis and cryptology. ( أبو يوسف يعقوب إبن إسحاق الكندي) (c Cryptanalysis (from the Greek kryptós, "hidden" and analýein, "to loosen" or "to untie" is the study of methods for Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" He gave the first known recorded explanation of cryptanalysis in A Manuscript on Deciphering Cryptographic Messages. Cryptanalysis (from the Greek kryptós, "hidden" and analýein, "to loosen" or "to untie" is the study of methods for In particular, he is credited with developing the frequency analysis method whereby variations in the frequency of the occurrence of letters could be analyzed and exploited to break ciphers (i. In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext. e. crypanalysis by frequency analysis). ^[24] This was detailed in a text recently rediscovered in the Ottoman archives in Istanbul, A Manuscript on Deciphering Cryptographic Messages, which also covers methods of cryptanalysis, encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic. ^[25]

Ahmad al-Qalqashandi (1355-1418) wrote the Subh al-a 'sha, a 14-volume encyclopedia which included a section on cryptology. Shihab al-Din abu 'l-Abbas Ahmad ben Ali ben Ahmad Abd Allah al-Qalqashandi (1355 or 1356 &ndash 1418 was a medieval Egyptian writer and mathematician born This information was attributed to Taj ad-Din Ali ibn ad-Duraihim ben Muhammad ath-Tha 'alibi al-Mausili who lived from 1312 to 1361, but whose writings on cryptology have been lost. The list of ciphers in this work included both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter. In Cryptography, a substitution cipher is a method of Encryption by which units of plaintext are substituted with Ciphertext according to a regular system In classical Cryptography, a transposition cipher changes one character from the Plaintext to another (to decrypt the reverse is done In Cryptography, plaintext is the information which the sender wishes to transmit to the receiver(s Also traced to Ibn al-Duraihim is an exposition on and worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which can not occur together in one word. The frequency of letters in text has often been studied for use in Cryptography, and Frequency analysis in particular

Geometry

See also: History of geometry

An engraving by Albrecht Dürer featuring Mashallah, from the title page of the De scientia motus orbis (Latin version with engraving, 1504). Geometry ( Greek γεωμετρία; geo = earth metria = measure arose as the field of knowledge dealing with spatial relationships Albrecht Dürer (ˈalbʀɛçt ˈdyʀɐ ( May 21, 1471 &ndash April 6, 1528) was a German painter, Printmaker Masha'allah ibn Atharī (c740-d815 AD was an eighth century Persian Jewish astrologer and astronomer from the city of Basra (now located in As in many medieval illustrations, the compass here is an icon of religion as well as science, in reference to God as the architect of creation

The successors of Muhammad ibn Mūsā al-Khwārizmī (born 780) undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. A compass or pair of compasses is a Technical drawing instrument that can be used for inscribing Circles or arcs They can also be used as Events By Place Byzantine Empire Constantine VI becomes Byzantine Emperor with Irene as guardian Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.

Al-Mahani (born 820) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu-Abdullah Muhammad ibn Īsa Māhānī, was a Persian mathematician and astronomer from Mahan, Kerman, Persia. Events By Place Asia Tahir, the son of a slave is rewarded with the governorship of Khurasan for supporting the Caliphate Al-Karaji (born 953) completely freed algebra from geometrical operations and replaced them with the arithmetical type of operations which are at the core of algebra today. (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. Events Europe First documented mention of the village of Aach in Rhineland-Palatinate, Germany. Arithmetic or arithmetics (from the Greek word αριθμός = number is the oldest and most elementary branch of mathematics used by almost everyone

Although Thabit ibn Qurra (known as Thebit in Latin) (born 836) contributed to a number of areas in mathematics, where he played an important role in preparing the way for such important mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-Euclidean geometry. (836 in Harran, Mesopotamia &ndash February 18, 901 in Baghdad) was an Arab astronomer, mathematician Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Events By Place Asia Abbasid caliph Al-Mutasim establishes a new capital at Samarra, Iraq. In Mathematics, the real numbers may be described informally in several different ways The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Spherical trigonometry is a part of Spherical geometry that deals with Polygons (especially Triangles on the Sphere and explains how to find relations Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry An important geometrical aspect of Thabit's work was his book on the composition of ratios. In this book, Thabit deals with arithmetical operations applied to ratios of geometrical quantities. The Greeks had dealt with geometric quantities but had not thought of them in the same way as numbers to which the usual rules of arithmetic could be applied. By introducing arithmetical operations on quantities previously regarded as geometric and non-numerical, Thabit started a trend which led eventually to the generalization of the number concept. Another important contribution Thabit made to geometry was his generalization of the Pythagorean theorem, which he extended from special right triangles to all right triangles in general, along with a general proof. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position In Mathematics, the Pythagorean theorem ( American English) or Pythagoras' theorem ( British English) is a relation in Euclidean geometry Two types of special right triangles appear commonly in geometry the "angle based" and the "side based" (or Pythagorean Triangles The former are characterised Two types of special right triangles appear commonly in geometry the "angle based" and the "side based" (or Pythagorean Triangles The former are characterised In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true ^[26]

Ibrahim ibn Sinan (born 908), who introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. Ibrahim ibn Sinan ibn Thabit ibn Qurra (908 Baghdad – 946 Baghdad was an Arab Mathematician and Astronomer who studied Geometry Events By Place Asia The Battle of Belach Mugna is fought Zhu Wen kills the last Tang Dynasty emperor The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer (sometimes) was a Persian mathematician, physicist and astronomer. Events By Place Asia Saadia Gaon compiles his Siddur (Jewish prayer book in Iraq. These mathematicians, and in particular Ibn al-Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface

Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. Geography (from Greek γεωγραφία - geografia) is the study of the Earth and its lands features inhabitants and phenomena For example Ibrahim ibn Sinan and his grandfather Thabit ibn Qurra both studied curves required in the construction of sundials. (836 in Harran, Mesopotamia &ndash February 18, 901 in Baghdad) was an Arab astronomer, mathematician Abu'l-Wafa and Abu Nasr Mansur pioneered spherical geometry in order to solve difficult problems in Islamic astronomy. Abu Nasr Mansur ibn Ali ibn Iraq (c 960 - 1036 was a was a Persian Muslim mathematician. Spherical geometry is the Geometry of the two- Dimensional surface of a Sphere. For example, to predict the first visibility of the moon, it was necessary to describe its motion with respect to the horizon, and this problem demands fairly sophisticated spherical geometry. The horizon ( Ancient Greek ὁ ὁρίζων, /ho horídzôn/ from ὁρίζειν, "to limit" is the apparent line that separates Finding the direction of Mecca (Qibla) and the time for Salah prayers and Ramadan are what led to Muslims developing spherical geometry. Mecca ˈmɛkə also spelled Makkah ˈmækə (in full Makkah Al-Mukarramah (Arabic mækːæ(t ælmʊkarˑamæ مكّة المكرمة, literally Honored Qiblah ( ar قبلة, also transliterated as Kiblah) is an Arabic word for the direction that should be faced when a Muslim prays during Ṣalāt ( Arabic: صلاة‎, pl ṣalawāt, Qur'anic Arabic: صلوة ṣalawah) (also munz in Pashto and Ramadan or Ramazan ( Arabic: رمضان Ramaḍān) is a Muslim religious observance that takes place during the ninth month of the Islamic ^[27][28]

Omar Khayyám (born 1048) was a Persian mathematician, as well as a poet. For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین layout and formatting it should ensure no clashes with the top of the infobox Along with his fame as a poet, he was also famous during his lifetime as a mathematician, well known for inventing the general method of solving cubic equations by intersecting a parabola with a circle. This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve. In addition he discovered the binomial expansion, and authored criticisms of Euclid's theories of parallels which made their way to England, where they contributed to the eventual development of non-Euclidean geometry. In Mathematics, the binomial theorem is an important Formula giving the expansion of powers of Sums Its simplest version says Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry Omar Khayyam also combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. In Mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with Quantitatively His work marked the beginnings of algebraic geometry^[29][30] and analytic geometry. Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry ^[23] Khayyam also made the first attempt at formulating a non-Euclidean postulate as an alternative to the Euclidean parallel postulate,^[31] and he was the first to consider the cases of elliptical geometry and hyperbolic geometry, though he excluded the latter. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry In traditional Logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive Elliptic geometry (sometimes known as Riemannian geometry) is a Non-Euclidean geometry, in which given a line L and a point In ^[32]

Persian mathematician Sharafeddin Tusi (born 1135) did not follow the general development that came through al-Karaji's school of algebra but rather followed Khayyam's application of algebra to geometry. (1135 - 1213 was a Persian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages) (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. He wrote a treatise on cubic equations, which represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the study of algebraic geometry.

In 1250, Nasīr al-Dīn al-Tūsī, in his Al-risala al-shafiya'an al-shakk fi'l-khutut al-mutawaziya (Discussion Which Removes Doubt about Parallel Lines), wrote detailed critiques of the Euclidean parallel postulate and on Omar Khayyám's attempted proof a century earlier. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین Nasir al-Din attempted to derive a proof by contradiction of the parallel postulate. Reductio ad absurdum ( Latin for "reduction to the absurd" also known as an apagogical argument, reductio ad impossibile ^[22] He was one of the first to consider the cases of elliptical geometry and hyperbolic geometry, though he ruled out both of them. Elliptic geometry (sometimes known as Riemannian geometry) is a Non-Euclidean geometry, in which given a line L and a point In ^[32]

His son, Sadr al-Din (sometimes known as "Pseudo-Tusi"), wrote a book on the subject in 1298, based on al-Tusi's later thoughts, which presented one of the earliest arguments for a non-Euclidean hypothesis equivalent to the parallel postulate. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry ^[22][33] Sadr al-Din's work was published in Rome in 1594 and was studied by European geometers. Rome ( Roma ˈroma Roma is the capital city of Italy and Lazio, and is Italy's largest and most populous city with more than 2 This work marked the starting point for Giovanni Girolamo Saccheri's work on the subject, and eventually the development of modern non-Euclidean geometry. Giovanni Girolamo Saccheri ( September 5, 1667 - October 25, 1733) was an Italian Jesuit priest and mathematician In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry ^[22] A proof from Sadr al-Din's work was quoted by John Wallis and Saccheri in the 17th and 18th centuries. John Wallis ( November 23, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the They both derived their proofs of the parallel postulate from Sadr al-Din's work, while Saccheri also derived his Saccheri quadrilateral from Sadr al-Din, who himself based it on his father's work. A Saccheri quadrilateral is a Quadrilateral with two equal sides perpendicular to the base ^[34]

The theorems of Ibn al-Haytham (Alhacen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Lambert quadrilateral and Saccheri quadrilateral, were the first theorems on elliptical geometry and hyperbolic geometry, and along with their alternative postulates, such as Playfair's axiom, these works marked the beginning of non-Euclidean geometry and had a considerable influence on its development among later European geometers, including Witelo, Levi ben Gerson, Alfonso, John Wallis, and Giovanni Girolamo Saccheri. TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین In Geometry, a quadrilateral is a Polygon with four sides or edges and four vertices or corners. A Lambert quadrilateral, or Ibn al-Haytham &ndashLambert quadrilateral, is a Hyperbolic Quadrilateral. A Saccheri quadrilateral is a Quadrilateral with two equal sides perpendicular to the base Elliptic geometry (sometimes known as Riemannian geometry) is a Non-Euclidean geometry, in which given a line L and a point In In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry Witelo - also known as Erazmus Ciolek Witelo, Witelon, Vitellio, Vitello, Vitello Thuringopolonis, Vitulon, Erazm Levi ben Gershom ( לוי בן גרשום) better known as Gersonides or the Ralbag (1288-1344 was a famous Rabbi, philosopher Mathematician Alfonso ( Italian and Spanish) Alfons ( Catalan and German) Afonso ( Portuguese John Wallis ( November 23, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the Giovanni Girolamo Saccheri ( September 5, 1667 - October 25, 1733) was an Italian Jesuit priest and mathematician ^[35]

Recently discoveries have shown that geometrical quasicrystal patterns were first employed in the girih tiles found in medieval Islamic architecture dating back over five centuries ago. Quasicrystals are structural forms that are both ordered and nonperiodic Girih tiles are a set of five Tiles that were used in the creation of tiling patterns for decoration of buildings in Islamic architecture. Islamic architecture has encompassed a wide range of both secular and religious styles from the foundation of Islam to the present day influencing the design and construction In 2007, Professor Peter Lu of Harvard University and Professor Paul Steinhardt of Princeton University published a paper in the journal Science suggesting that girih tilings possessed properties consistent with self-similar fractal quasicrystalline tilings such as the Penrose tilings, predating them by five centuries. Peter James Lu PhD (陸述義 b 1978 in Cleveland, OH is a post-doctoral research fellow in the Department of Physics at Harvard University, Cambridge Massachusetts Paul J Steinhardt is the Albert Einstein Professor of Science at Princeton University and a Professor of Theoretical physics. Princeton University is a private Coeducational research university located in Princeton, New Jersey. In Mathematics, a self-similar object is exactly or approximately similar to a part of itself (i A fractal is generally "a rough or fragmented geometric shape that can be split into parts each of which is (at least approximately a reduced-size copy of the whole" A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of Prototiles named after Roger Penrose, who investigated these sets ^[36][37]

Mathematical induction

The first known proof by mathematical induction was introduced in the al-Fakhri written by Al-Karaji around 1000 AD, who used it to prove arithmetic sequences such as the binomial theorem, Pascal's triangle, and the sum formula for integral cubes. Mathematical induction is a method of Mathematical proof typically used to establish that a given statement is true of all Natural numbers It is done by proving that (or) (c 953 in Karaj or Karkh &ndash c 1029 was a 10th century Persian Muslim mathematician and engineer. In Mathematics, an arithmetic progression or arithmetic sequence is a Sequence of Numbers such that the difference of any two successive members In Mathematics, the binomial theorem is an important Formula giving the expansion of powers of Sums Its simplest version says \begin{matrix}&&&&&1\\&&&&1&&1\\&&&1&&2&&1\\&&1&&3&&3&&1\\&1&&4&&6&&4&&1\end{matrix The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Arithmetic and Algebra, the cube of a number n is its third power &mdash the result of multiplying it by itself three times ^[38][39] His proof was the first to make use of the two basic components of an inductive proof, "namely the truth of the statement for n = 1 (1 = 1³) and the deriving of the truth for n = k from that of n = k - 1. The meaning of the word truth extends from Honesty, Good faith, and Sincerity in general to agreement with Fact or Reality "^[40]

Shortly afterwards, Ibn al-Haytham (Alhazen) used the inductive method to prove the sum of fourth powers, and by extension, the sum of any integral powers, which was an important result in integral calculus. TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized In Arithmetic and Algebra, the fourth power of a number n is the result of multiplying n by itself four times The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives He only stated it for particular integers, but his proof for those integers was by induction and generalizable. ^[41][42]

Ibn Yahyā al-Maghribī al-Samaw'al came closest to a modern proof by mathematical induction in pre-modern times, which he used to extend the proof of the binomial theorem and Pascal's triangle previously given by al-Karaji. مغربي، السموءل بن يحي، also known as Samau'al al-Maghribi (c Al-Samaw'al's inductive argument was only a short step from the full inductive proof of the general binomial theorem. ^[43]

Number theory

In number theory, Ibn al-Haytham solved problems involving congruences using what is now called Wilson's theorem. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes TemplateInfobox Muslim scholars --> ( Arabic: ابو علی، حسن بن حسن بن هيثم Latinized See Congruence (geometry for the term as used in elementary geometry In Mathematics, Wilson's theorem states that p > 1 is a Prime number If and only if (p-1!\ \equiv\ -1\ (\mbox{mod}\ p In his Opuscula, Ibn al-Haytham considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem. The Chinese remainder theorem is a result about congruences in Number theory and its generalizations in Abstract algebra. Another contribution to number theory is his work on perfect numbers. In mathematics a perfect number is defined as a positive integer which is the sum of its proper positive Divisors that is the sum of the positive divisors excluding In his Analysis and synthesis, Ibn al-Haytham was the first to discover that every even perfect number is of the form 2ⁿ⁻¹(2ⁿ − 1) where 2ⁿ − 1 is prime, but he was not able to prove this result successfully (Euler later proved it in the 18th century). In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 ^[44]

Recreational mathematics

In recreational mathematics, magic squares were known to Arab mathematicians, possibly as early as the 7th century, when the Arabs got into contact with Indian or South Asian culture, and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games. In Recreational mathematics, a magic square of order n is an arrangement of n ² numbers usually distinct Integers in a square, such The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects It has also been suggested that the idea came via China. The first magic squares of order 5 and 6 appear in an encyclopedia from Baghdad circa 983 AD, the Rasa'il Ihkwan al-Safa (the Encyclopedia of the Brethern of Purity); simpler magic squares were known to several earlier Arab mathematicians. Baghdad (بغداد) is the Capital of Iraq and of Baghdad Governorate, with which it is also coterminous The Encyclopedia of the Brethren of Purity (also variously known as the Epistles of the Brethren of Sincerity, the Epistles of the Brethren of Purity or Epistles ^[45]

The Arab mathematician Ahmad al-Buni, who worked on magic squares around 1200 AD, attributed mystical properties to them, although no details of these supposed properties are known. Ahmad ibn ‘Ali ibn Yusuf al-Buni (أحمد البوني (died 1225 was a well known Arab Sufi and writer on the Esoteric value of letters and topics There are also references to the use of magic squares in astrological calculations, a practice that seems to have originated with the Arabs. ^[45]

Trigonometry

The early Indian works on trigonometry were translated and expanded in the Muslim world by Arab and Persian mathematicians. Indian mathematics &mdashwhich here is the mathematics that emerged in South Asia zero, Negative numbers, Arithmetic, and Algebra. Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. The term Muslim world (or Islamic world) has several meanings This is a list of scientists and scholars from the Arab World and Islamic Spain ( Al-Andalus) that lived from antiquity up until the beginning Classical (pre-modern Era The following is a non-comprehensive list of Iranian scientists and engineers that lived from antiquity up until the beginning of the modern Muhammad ibn Mūsā al-Khwārizmī produced tables of sines and tangents, and also developed spherical trigonometry. Spherical trigonometry is a part of Spherical geometry that deals with Polygons (especially Triangles on the Sphere and explains how to find relations By the 10th century, in the work of Abū al-Wafā' al-Būzjānī, Muslim mathematicians were using all six trigonometric functions, and had sine tables in 0. 25° increments, to 8 decimal places of accuracy, as well as tables of tangent values. Abū al-Wafā' also developed the trigonometric formula sin 2x = 2 sin x cos x.

Al-Jayyani (989–after 1079) of al-Andalus wrote the first treatise on spherical trigonometry, entitled The book of unknown arcs of a sphere, which "contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle. Abu Abd Allah Muhammad ibn Muadh Al-Jayyani, shortened to Al-Jayyani ( 989, Cordova, Al-Andalus – 1079, Jaen, Al-Andalus Al-Andalus (الأندلس was the Arabic name given to those parts of the Iberian Peninsula governed by Muslims or Spherical trigonometry is a part of Spherical geometry that deals with Polygons (especially Triangles on the Sphere and explains how to find relations Two types of special right triangles appear commonly in geometry the "angle based" and the "side based" (or Pythagorean Triangles The former are characterised The law of sines ( sines law sine formula sine rule) in Trigonometry, is a statement about any Triangle in a plane Spherical trigonometry is a part of Spherical geometry that deals with Polygons (especially Triangles on the Sphere and explains how to find relations A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line " This treatise later had a "strong influence on European mathematics", and his "definition of ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus. A ratio is an expression which compares quantities relative to each other Johannes Müller von Königsberg ( June 6, 1436 &ndash July 6, 1476) known by his Latin Pseudonym Regiomontanus ^[46]

Omar Khayyám (1048-1131) solved cubic equations using approximate numerical solutions found by interpolation in trigonometric tables. For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین This article discusses cubic equations in one variable For a discussion of cubic equations in two variables see Elliptic curve.

All of these earlier works on trigonometry treated it mainly as an adjunct to astronomy; perhaps the first treatment as a subject in its own right was by Bhaskara II and Nasir al-Din al-Tusi (13th century). Bhaskara (1114 &ndash 1185 also known as Bhaskara II and Bhaskara Achārya ("Bhaskara the teacher" was an Indian mathematician Nasir al-Din al-Tusi stated the law of sines and provided a proof for it, and also listed the six distinct cases of a right angled triangle in spherical trigonometry. The law of sines ( sines law sine formula sine rule) in Trigonometry, is a statement about any Triangle in a plane

Ghiyath al-Kashi (14th century) gives trigonometric tables of values of the sine function to four sexagesimal digits (equivalent to 8 decimal places) for each 1° of argument with differences to be added for each 1/60 of 1°. (or, Persian: غیاث‌الدین جمشید کاشانی (c Sexagesimal ( base-sixty) is a Numeral system with sixty as the base. Ulugh Beg (14th century) also gives accurate tables of sines and tangents correct to 8 decimal places. Ulugh Beg ( Chaghatay / - also Uluğ Bey, Ulugh Bek and Ulug Bek) (c

The method of triangulation, which was unknown in the Greco-Roman world, was also first developed by Muslim mathematicians, who applied it to practical uses such as surveying. In Trigonometry and Geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either In modern Olympic and amateur Wrestling, Greco-Roman wrestling is a particular style and variation Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between ^[47]

See also

• List of Muslim mathematicians
• Latin translations of the 12th century
• Islamic science
• Islamic Golden Age
• Inventions in the Muslim world

Notes

Further reading

External links

• Hogendijk, Jan P. (January 1999). Bibliography of Mathematics in Medieval Islamic Civilization.