#Muḥammad ibn Mūsā al-Khwārizmī

[quordleona03]

The reason every century is supposed to start with the year one (but really starts with the year __00) is this:

The calendar we base the CE year on was devised in Diocletian 247, the year of the consulship of Probus Junior, which is the year we now refer to as 525 CE, by Dionysius Exiguus of Tomis, a monk born in Scythia Minor (Romania/Bulgara, on the modern map of Europe). Dionysius was unaware he was devising a millennial calendar: he thought he was working out a table for the dates Easter would fall on, in the years Diocletian 248-352, but he didn't want the year-count in the Easter table to make reference to a pagan Emperor: instead Dionysius worked out the year in which he thought Jesus must have been born and counted the years from that for his Easter table, so that Diocletian 247 in the previous Easter table was followed by anno Domini nostri Jesu Christi 532.

(Years were counted from Diocletian's reign because he was recognised as the Emperor who stabilised the Empire after a 50-year period during which there were 26 claimants to be Emperor and the Empire itself had split into three factions.)

People argue that 2020 can't be the first year of a new decade because this would mean there was a nine-year "decade" in 1-9 CE. Well, yes, except there wasn't, because in the years 1-9 CE no one was using Dionysius Exiguus's calendar, strangely enough.

You might ask: why Dionysius Exiguus didn't begin his Anno Domini calender with the Year Zero - why he calculated Year 1 Anno Domini and why Bede in his Historia ecclesiastica gentis Anglorum (731 CE) assumed that the Before Christ year-count started in year-one before Year 1 A.D. (Bede wrote: ante [...] incarnationis dominicae tempus anno sexagesimo, "in the sixtieth year before the time of the Lord's incarnation").

While nihil/nothing was known as an option when doing numerical calculations using Roman numerals (the earliest recorded evidence [for arithmetic using Roman numerals] that arithmeticians understood when you take III + V away from VIII you have to indicate the nihil result somehow, is from recorded calculations to predict the date of Easter). But the number zero was introduced as a concept to Europe in a 12th-century translation into Latin of a 9th-century Arabic text by Muḥammad ibn Mūsā al-Khwārizmī, on decimal mathematics. Decimal mathematics inlcuding the number 0 were in use in India (we know from Sanskrit manuscripts) from probably the 5th century CE onward, but not in Europe for another seven centuries.

Bede didn't have the concept of a Year Zero. Nor did Dionysius Exiguus, though he would probably have been more interested in the idea than Bede.

But we do.

Which means in the Common Era calendar, years ending in 0 are the start of a new decade, and years ending in 00 are the start of a new century.

But whether you start counting at one or at zero, the century that began anno Domini nostri Jesu Christi 600 in the Dionysius Exiguus calendar would have been the beginning of the 7th century of the Commone Era calendar.

Brits call the floor at ground level the ground floor. We're logical like that. So the floor above the ground floor is the first floor that's not the ground floor.

Americans call the floor at ground level. the first floor. They're logical like that. So the next floor above the ground floor is the second floor.

The common-era calendar, though devised in Scythia Minor in the year Diocletian 247, is numbered like an American building: century zero is at ground level and so that zero ground level century is the first century.

i hate hate hate that the “NINEteenth century” is talking about the EIGHTEEN hundreds. i know why this happens mathematically and stuff. but isn’t it just so fucked up? doesn’t it feel so wrong? dont you have to fight with your brain to reconcile the difference? is this not a sign of humanity’s eternal despair?

[hesperocyon-lesbian]

me: anyway the algorithm basically recommends content based on what you’ve watched, a whole bunch of different apps do this

medieval mathematician Muḥammad ibn Mūsā al-Khwārizmī: they named WHAT after me????

[de-temple]

Algorithm - Wikipedia

"Etymology

Around 825 AD, Persian scientist and polymath Muḥammad ibn Mūsā al-Khwārizmī wrote kitāb al-ḥisāb al-hindī ("Book of Indian computation") and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ("Addition and subtraction in Indian arithmetic"). Both of these texts are lost in the original Arabic at this time. However, his other book on algebra remains.[1]

In the early 12th century, Latin translations of said al-Khwarizmi texts involving the Hindu–Arabic numeral system and arithmetic appeared: Liber Alghoarismi de practica arismetrice (attributed to John of Seville) and Liber Algorismi de numero Indorum (attributed to Adelard of Bath).[2] Hereby, alghoarismi or algorismi is the Latinization of Al-Khwarizmi's name; the text starts with the phrase Dixit Algorismi ("Thus spoke Al-Khwarizmi").[3]

Around 1230, the English word algorism is attested and then by Chaucer in 1391, English adopted the French term.[4][5][clarification needed] In the 15th century, under the influence of the Greek word ἀριθμός (arithmos, "number"; cf. "arithmetic"), the Latin word was altered to algorithmus.[citation needed]

Definition

For a detailed presentation of the various points of view on the definition of "algorithm", see Algorithm characterizations."

https://en.wikipedia.org/wiki/Algorithm#:~:text=Etymology%5Bedit,Algorithm%20characterizations.

[forgottengenius]

Al-Khwarizmi : The father of algebra

None of the great achievements of modern science would be possible without the mathematisation of science and the development of algebra. The word algebra stems from the Arabic word al-jabr, which has its roots in the title of a 9th century manuscript written by the mathematician Al-Khwarizmi.

Al-Khwarizmi's Kitab al-mukhtasar fi hisab al-jabr wal-muqabala (The Compendious Book on Calculation by Completion and Balancing) was a pioneering piece of work - offering practical answers for land distribution, rules on inheritance and distributing salaries. In this episode of Science in the Golden Age, theoretical physicist, Jim al-Khalili explores Al-Khwarizmi's 9th century treatise that also underpins the science of flight and the engineering behind the fastest car in the world.

Originally Persian, Al-Khwarizmi spent his academic life in the city of Baghdad from where the Abbasid caliphs ruled and established the Bayt al-Hikma (The House of Wisdom), a renowned centre of learning. With Professor Ramazan Sesen and Dr Peter Starr, Jim discusses the origins of the House of Wisdom and how the translation of Greek, Persian and other texts was central to the progressive scientific and mathematical revolution that originated in Baghdad.

And, in the Sulemaniye Library in Istanbul, Jim uncovers a rare text by Al-Kindi, a philosopher, polymath, and musician – and perhaps the world's earliest mathematical code breaker.

Source: Al Jazeera

[mszegedy]

So this isn’t gonna be a long and well-researched post or anything but I’m just surprised that the word for “zero” in most languages is a loanword. Like yes in mathematics and counting, it’s a relatively new and sophisticated concept that had to be spread from culture to culture, but the quantity itself has a name in most languages. In English, it’s “none”. But instead, we use “zero”, which is ultimately from Arabic صِفْر‎ (ṣifr), which originally meant “empty” before it came to mean “zero”. In Hungarian, we say nulla, which is ultimately from Latin nulla, meaning “none”. Better, but why not use native Hungarian semennyi (”none”)?

Sometimes words are loaned where Language X has a word for Concept A, and then Language Y will loan X’s word for it to mean “X’s version of A”. Like how in English, “queso” is “Hispanic cheese”, “naan” and “chai” are “Indian bread” and “Indian tea”, and “anime” is “Japanese animation”, but in Spanish, Hindi, and Japanese, the words they were loaned from mean “cheese”, “bread”, “tea”, and “animation” respectively. Was zero “Arabic/Persian empty” for the Europeans who originally loaned ṣifr? Was it “Latin/science none” for the Hungarians who loaned nulla?

Another interesting question is why it was named “empty” in Arabic at all. The invention of zero is usually credited to the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī, who published many invaluable mathematical texts in the early 800s. (The word “algorithm” comes from his surname. Imagine being so foundational to a field that your name becomes distorted into the word for a fundamental concept in it that’s in use over a thousand years later.) In his text where he basically invented algebra, he wrote about zero as a concept. (Can’t do algebra without zero.) But the person who actually named zero in Arabic was a Persian encyclopedist who lived over a hundred years later, Muḥammad ibn Aḥmad al-Khwārizmī. He was also the one who came up with the idea to symbolize it with a circle. He used the circle as a placeholder for the tens place specifically. If someone wanted to figure out what inspired him to name it “empty”, they’d have to look into what he was reading. I can’t even get ahold of a translation of the big al-Khwārizmī’s text on algebra with just a cursory search. Isn’t it supposed to be public domain by now?

You’d also have to look at what alternative ways there are to name it in Arabic. (I’m not well-studied on Arabic, so anything that follows may be completely wrong.) Arabic doesn’t have a specific word for “none”. If you want to say “there are none”, then you say لا يوجد (lā yūjad, “there aren’t”). The negative particle is لا (lā). It would be a bad idea to make that stand for zero. It would be like calling zero “not” or “no”. Words like “nothing” and “not one” are formed with لا as well, so it’s not so neat to make those stand for zero, either. Muḥammad ibn Aḥmad al-Khwārizmī was probably working with the best he had.

(Incidentally, Persian has a word for “none”, هیچیک (hičyek), essentially “none of one”. Just هیچ (hič) could have also done the job. Oh well.)

[ftsharp]

In 820, Muḥammad ibn Mūsā al-Khwārizmī invented algebra for solving linear and quadratic equations. Poetry by Tom Sharp.

[vbeyaz]

Al-Khwârizmî : Muḥammad ibn Mūsā al-Khwārizmī, généralement appelé Al-Khwârizmî, né dans les années 780, probablement à Khiva dans la région du Khwarezm, dans l'actuel Ouzbékistan, mort vers 850 à Bagdad, est un mathématicien, géographe, astrologue et astronome persan, membre de la Maison de la sagesse de Bagdad.  Des études situent sa famille dans la communauté turque du Khwarezm. Il est consideré comme un mathématicien arabisé. Il existe de nombreuses traces de ses travaux scientifiques. Mathématicien, historien et géographe astronome , condideré comme « le père de l’algèbre et le premier vulgarisateur du système décimal positionnel » . Membre de la Maison de la sagesse de Bagdad. Ses écrits, rédigés en langue arabe, puis traduits en latin à partir du xiie siècle, ont permis l'introduction de l'algèbre en Europe. Sa vie s'est déroulée en totalité à l'époque de la dynastie abbasside. Son nom latinisé est à l’origine du mot algorithme et le titre de l'un de ses ouvrages (Abrégé du calcul par la restauration et la comparaison) est à l'origine du mot algèbre, discipline mathématique connue depuis l’antiquité. L'utilisation des chiffres arabes et leur diffusion dans le Moyen-Orient et en Europe serait dues à un autre de ses livres nommé Traité du système de numération des Indiens qui fut diffusé via la langue arabe dans tout l'empire abbasside. Al-Khawarizmi a classifié les algorithmes existants, en particulier selon leurs critères de terminaison. Les premiers algorithmes répertoriés ont été retrouvés dans des régions qui les utilisaient pour des applications pratiques (mesures, transactions commerciales, architecture...), à Babylone. Il est l'auteur de trois ouvrages consacrés à des instruments : un ouvrage sur le cadran solaire, un livre sur la réalisation de l'astrolabe et un livre sur l'utilisation de l'astrolabe. Son ouvrage sur le calendrier juif est un des plus anciens exposé sur le sujet. Il y expose le découpage de l'année, la position des étoiles à certaines moments clefs. Il est l'auteur des premières tables pour régler les heures des prières de la journée. Al-Khwârizmî est astrologue.prédit la longue durée de vie calife. https://www.instagram.com/p/CesqRK9N-abVGxjoj5aaW94ceibp1F8uUU4Q5s0/?igshid=NGJjMDIxMWI=

[sorwaruddin-blog]

Born in 780 AD in present day Iran, Muḥammad ibn Mūsā al-Khwārizmī  was a Muslim scholar who produced works in mathematics, astronomy and geography and under the patronage of the Abbasid Caliphate. Around 820 AD he was appointed as the astronomer and head of the House of Wisdom in Baghdad.

Long before London or Frankfurt. Baghdad was a cornerstone of mathematical excellence, it was a powerhouse which flourished during the Abbasid period. He produced various linear and quantum theories, many of which are used to this present day, he was a founder of Cryptoanalysis and expanded on the works of the Greeks. Isn't it a shame that Cairo, Baghdad and Athens are no longer recognised for their immense contributions.

Gone, but not forgotten. May their legacy live on. Great men were not destined to live forever.

[panoramadelafisica-2017-1-blog]

04 - الجبر

Grata la voz del agua a quien abrumaron negras arenas, grato a la mano cóncava el mármol circular de la columna, gratos los finos laberintos del agua entre los limoneros, grata la música del zéjel, grato el amor y grata la plegaria dirigida a un Dios que está solo, grato el jazmín.

Vano el alfanje ante las largas lanzas de los muchos, vano ser el mejor. Grato sentir o presentir, rey doliente, que tus dulzuras son adioses, que te será negada la llave, que la cruz del infiel borrará la luna, que la tarde que miras es la última.

Alhambra - Jorge Luis Borges (1899 - 1986)

En esta clase estudiamos un importantísimo legado del mundo árabe: el álgebra (del árabe para "recomponer"). En un acto de genialidad extraordinaria, el pensador persa Muḥammad ibn Mūsā al-Khwārizmī (780 - 850) se dió cuenta de que podía expresar las matemáticas a través de un lenguaje preciso, lógico, riguroso y conciso en lugar de sólo en términos geométricos como lo habían hecho los griegos. Esta genialidad dio origen al lenguaje de la Física moderna. Aún en tiempos de Newton las matemáticas se formulaban al estilo geométrico griego clásico (como se puede apreciar al leer sus Principia). Hoy en día hemos llegado al extremo contrario. Podemos comprender la geometría de cosas que no podemos imaginar (como espacios curvos de dimensionalidades más altas) utilizando el lenguaje algebraico heredado del ya milenario al-Khwārizmī. Nosotros utilizamos estas ideas con un propósito sencillo pero importante: comprender cómo manejar las unidades con las que describiremos el Universo. Los dejo con el video "Nature by Numbers" en el que se exploran sencillas relaciones matemáticas que se suelen dar en forma aproximada en algunos seres vivos.

[forgottengenius]

'Abd al-Hamīd ibn Turk

ʿAbd al-Hamīd ibn Turk (fl. 830), known also as ʿAbd al-Hamīd ibn Wase ibn Turk Jili was a ninth-century Turkic Muslim mathematician. Not much is known about his biography. The two records of him, one by Ibn Nadim and the other by al-Qifti are not identical. However al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk Jili. Jili means from Gilan.[1]

He wrote a work on algebra of which only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived.

 He 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.[2] The manuscript gives exactly the 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.[2] The similarity between these two works has led some historians to conclude that algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.[2]

[truthseekerro]

7 inventii ale musulmanilor

http://ro.truth-seeker.info/nestemate-ale-islamului/7-inventii-ale-musulmanilor/

7 inventii ale musulmanilor

7  inventii ale musulmanilor

  Musulmanii au fost animati permanent de crezul necesitatii dezvoltarii lor, de invataturile Profetului Muhammad in care spunea ca musulmanul trebuie sa vina mereu cu idei noi, cu solutii noi, folositoare omenirii.

Ascultand sfaturile Profetului, musulmanii au adus de-a lungul timpului contributii extrem de importante la dezvoltarea omenirii. Mai jos vom enumera sapte dintre cele mai utilizate inventii ale musulmanilor:

  7 MARI INVENTII ale Musulmanilor

Lumea musulmana a influentat dezvoltarea umanitatii in toate aspectele sale. Oamenii de stiinta musulmani au fost prolifici si au facut descoperiri importante, cu mult inaintea descoperirilor petrecute in Occident. De asemenea, cafeaua, care este o bautura orientala, nu este doar cea mai iubita bautura din lume, dar mai ales un simbol cultural care vorbeste despre vietile si interactiunile noastre astazi. Acestea sunt 7 dintre cele mai infleunte inventii si descoperiri care apartin lumii Orientale.

1. Cafeaua

Istoria acestei bauturi iubite in intreaga lume, fara de care nu ne putem incepe ziua, multi dintre noi, ne poarta in vremea unui arab pe nume Khalid, care isi pastea caprele in regiunea Kaffa, din Sudul Etiopiei. Khalid a observat ca animalele sale devenisera mai vioaie, dupa ce au pascut anumite boabe. El a fiert acest boabe si a obtinut cafeaua.

La inceput, cafeaua a fost adusa din Etiopia in Yemen, acolo unde sufitii o beau astfel incat sa reziste treji toata noaptea, pentru a se ruga, in diverse ocazii.

Pana la sfarsitul secolului al 15-lea, cafeaua a ajuns la Mecca si in Turcia si de acolo a ajuns la Venetia, in anul 1645. In anul 1650, cafeaua a fost adusa si in Anglia, de catre un turc pe nume Pasqua Rosee, care a deschis primul magazin de cafea, pe strada Lombard din Londra.

  2. Camera Obscura

Grecii antici credeau, in mod fals, ca ochii nostri emit raze care ne ajuta sa vedem. Prima persoana care si-a dat seama ca de fapt lumina este cea care intra in ochii nostri, a fost matematicianul, fizicianul si astronomul musulman care a trait in secolul 10, Ibn al-Haitham.

  El este cel care a inventat prima camera obscura, observand cum lumina patrundea prin gaura unor obloane de la geamuri. Cu cat este mai mica gaura, cu atat este mai buna imaginea care se creeaza. El a devenit inventatorul camerei obscure, iar denumirea isi afla etimologia de la cuvantul arab ce denumeste o camera racoroasa si intunecoasa – CAMARA (cuvantul exista si in limba romana!). De asemenea, Ibn al-Haitham este primul cercetator caruia i se crediteaza faptul de a fi mutat studiul din fizica dinspre meditatia filosofica, teoretica, inspre experiment.

    3. Jocul de Sah

O forma de sah se juca in India Antica, dar jocul s-a dezvoltat in forma pe care o cunoastem astazi, in Persia. De acolo s-a extins in intreaga Europa – prin intermediul musulmanilor care se gaseau in Peninsula Iberica, in secolul 10.

  4. Numerotarea

Sistemul de numarare pe care il folosim in intreaga lume este probabil indian la origine, dar numerotarea este araba. A aparut prima dat in scrierile matematicienilor musulmani Muḥammad ibn Mūsā al-Khwārizmī si Al-Kindi, in jurul anului 825.

Algebra a fost denumita dupa numele cartii lui al-Khwarizmi: Al-Jabr wa-al-Muqabilah. Lucrarile matematicienilor arabi au fost duse in Europa 300 de ani mai tarziu, de catre matematicianul italian Fibonacci.

  5. Parasuta

Cu mult timp inaintea experimentelor zburatoare pe care le faceau Fratii Wright, un poet, astronom, inginer si muzician musulman, pe nume Abbas ibn Firnas, a facut mai multe incercari pentru a construi un aparat de zbor. In anul 825 el a sarit de pe minaretul Moscheei din Cordoba, folosindu-se de o inventie facuta din lemn si o panza de mantie. Spera ca va pluti precum o pasare. Nu s-a intamplat acest lucru, dar mantia s-a umflat si astfel se pare ca el a creat prima parasuta; datorita mantiei sale zburatoare, saltul la inaltime nu l-a costat pe Abbas ibn Firnas, decat cateva rani minore.

In anul 875 si-a perfectionat inventia si a folosit matase in loc de panza de mantie. A sarit de pe un munte si a reusit sa stea in aer pentru 10 minute pentru ca apoi sa se prabuseasca. A ajuns la concluzia corecta ca acest lucru s-a datorat faptului ca nu a adaugat o „coada” dispozitivului sau, care sa il ajute in stabilirea echilibrului.

Aeroportul International din Bagdad si un crater de pe Luna poarta numele acestui temerar inventator musulman.

  6. Pamantul este rotund!

Pana in secolul 9, multi invatati musulmani stiau deja ca pamantul este o sfera. Dovada, spunea astronomul Ibn Hazm este aceea ca Soarele este mereu vertical fata de un punct particular de pe Pamant. Aceasta afirmatie a fost facuta cu 500 de ani inaintea lui Galileo.

Calculele astronomilor musulmani erau atat de acurate incat, in secolul 9 ei au ajuns la concluzia ca circumferinta Pamantului este 40,253 de km, o estimare foarte apropiata de circumferinta reala, care stim astazi, este de 40,075 de km.

  7. Instrumente chirurgicale si alte descoperiri medicale

Multe instrumente chirurgicale au un design asemantor cu cele create de chirurgul musulman al-Zahrawi, in secolul 10. El a creat in jur de 200 de instrumente chirurgicale, iar utilitatea lor este recunoscuta si astazi in lumea medicala.

Musulmanii au si alte realizari in lumea medicala. In secolul 13, medicul Ibn Nafis a descris circulatia sangelui in organism cu 300 de ani inaintea lui William Harvey, care este creditat pentru aceasta informatie. Medicii musulmani au inventat anestezicul si alte dezinfectante dar si unelte pentru a extrage cataracta

via @The Independent.co.uk

[cherryjams]

[ftsharp]

In 820, Muḥammad ibn Mūsā al-Khwārizmī invented algebra for solving linear and quadratic equations. Poetry by Tom Sharp.

[wuggen]

Don't even need to go to another world for the first one. The word "algorithm" is the result of a multiple-languages-long chain of phonetic corruptions from the name of Muḥammad ibn Mūsā al-Khwārizmī, a Persian mathematician who also laid the foundations for (and gave the name to) modern-day algebra with his book the Al-jabr

In another world, Algorithm is a men's name (shortened to Al). Allergy is a women's name (also shortened to Al)

[forgottengenius]

Muḥammad ibn Mūsā al-Khwārizmī

Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī earlier transliterated as Algoritmi or   was a Persian[2][5] mathematician, astronomer and geographer during the Abbasid Empire, a scholar in the House of Wisdom in Baghdad. In the twelfth century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world.[4] His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources.[6] He revised Ptolemy's Geography and wrote on astronomy and astrology. Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations. Algorism and algorithm stem from Algoritmi, the Latin form of his name.[7] His name is

Life

He was born in a Persian[2][5] family, and his birthplace is given as Chorasmia[9] by Ibn al-Nadim.

Few details of al-Khwārizmī's life are known with certainty. His name may indicate that he came from Khwarezm (Khiva), then in Greater Khorasan, which occupied the eastern part of the Greater Iran, now Xorazm Province in Uzbekistan. Al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul),[10] a viticulture district near Baghdad. However, Rashed[11] suggests:

There is no need to be an expert on the period or a philologist to see that al-Tabari's second citation should read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are two people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic 'و' for the article 'and'] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning the personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made. Recently, G. J. Toomer ... with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader.

Regarding al-Khwārizmī's religion, Toomer writes:

Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he was an adherent of the old Zoroastrian religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwārizmī's Algebra shows that he was an orthodox Muslim, so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.[12]

Ibn al-Nadīm's Kitāb al-Fihrist includes a short biography on al-Khwārizmī, together with a list of the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city, as did Al-Khwārizmī. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Maʾmūn, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts. D. M. Dunlop suggests that it may have been possible that Muḥammad ibn Mūsā al-Khwārizmī was in fact the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā.[13][year missing]

Contributions

Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabalaالكتاب المختصر في حساب الجبر والمقابلة). On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm". Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.

 Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle East. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa. He also wrote on mechanical devices like the astrolabe and sundial. He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.[14]When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.[15]

Algebra 

Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة‎, 'The Compendious Book on Calculation by Completion and Balancing') is a mathematical book written approximately 830 CE. The book was written with the encouragement of the Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance.[16] The term algebra is derived from the name of one of the basic operations with equations (al-jabr, meaning completion, or, subtracting a number from both sides of the equation) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.[17]

It provided an exhaustive account of solving polynomial equations up to the second degree,[18] and discussed the fundamental methods of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.[19]

Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)

squares equal roots (ax2 = bx)

squares equal number (ax2 = c)

roots equal number (bx = c)

squares and roots equal number (ax2 + bx = c)

squares and number equal roots (ax2 + c = bx)

roots and number equal squares (bx + c = ax2)

by dividing out the coefficient of the square and using the two operations al-jabr (Arabic: الجبر‎ "restoring" or "completion") and al-muqābala ("balancing"). Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x2 = 40x − 4x2 is reduced to 5x2 = 40x. Al-muqābala is the process of bringing quantities of the same type to the same side of the equation. For example, x2 + 14 = x + 5 is reduced to x2 + 9 = x.

The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an 1831 translation)

"If some one say: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts."[16]

In modern notation this process, with 'x' the "thing" (shay') or "root", is given by the steps,

Let the roots of the equation be 'p' and 'q'. Then , and

So a root is given by

Several authors have also published texts under the name of Kitāb al-jabr wa-l-muqābala, including |Abū Ḥanīfa al-Dīnawarī, Abū Kāmil Shujā ibn Aslam, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī.

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. 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., 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."[20]

R. Rashed and Angela Armstrong write:

"Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus' Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."[21]also the origin of (Spanish) guarismo[8] and of (Portuguese) algarismo, both meaning digit.

[sleepy-toasted-bunny]

Part of me wants to argue that of it's a docudrama then the actor should look like the historical figure but... really? Not even then unless it's integral to the person's being.

I will use Hamilton as an example of being a bad use of this... The historical Hamilton had slaves, why would you cast a black person if not /just/ to piss off conservatives.

Also take the opportunity to uplift actual historical PoC figures like Mae Carol Jemison (first African American woman in space), Gladys West (helped make GPS possible), Muḥammad ibn Mūsā al-Khwārizmī (helped organise algebra into a more cohesive math), or whoever else (I've spent too much time trying to get Google to show me a variety of PoC scientists, but it mainly wants to show me black Americans and I wanted a truly diverse list, I had to remember the Algebra guy on my own).

I am officially done with totally-not-racist-ppl who do all the “actor of colour can’t play this character cause poc weren’t invented in XY century”. So basically I was going through Les Miserables tags around here and found some posts about Javert and all the “cannot be played by poc” shit going on. Let me tell you something…

If something is meant as strictly historical thing with exact depiction of the period with strong emphasis on the actual state of the society, then, yes, maybe poc should not play aristocrats or sth. I know not much about how it actually was like in period like XIX century, but I guess it was pretty racist with some exceptions so… Yeah. And why exactly should they not play aristocrats or such like? Not because they “weren’t invented”, but because it may twist the historical truth and diminish the suffering of people of colour back then. It is THE ONLY reason why in certain shows or whatever poc should not play some roles. THE ONLY. To preserve the memory of how shitty the period in question was for them and to show it was bad and white ppl were horrible to them. Let’s not forget that to be better now. Let’s keep it in mind and never forget about it. And I say it ONLY about very strictly historical things focused on such issues solely or strongly.

But when we speak of a musical based on a work of fiction then why the hell not? I mean, Les Mis as a book shows the society of the period, sure, but the colour issues are not there or should I say, are not the point for the author. The poverty is. So I think even in a regular show or film based on Hugo’s book it’s fine to cast actors of colour. So even more so when it comes to a staged musical which is a form of art so damn unrealistic with people singing instead of talking, having microphones and costumes made of probably not period wise materials! HOW CAN ANYONE ARGUE ABOUT POC IN PERIOD MUSICAL BEING UNREALISTIC? Like, THE WHOLE THING is unrealistic and make-believe with props, invisible blood, invisible RIVER… Come on! It’s theatre, not a history lesson! 

And another thing. I probably should remind everybody that diversity is important cause the racism is still there and it can be well hidden. You know, actors do not get roles for no apparent reason or get only certain sidekick/stereotypical roles cause they are poc. So go away with your “they weren’t invented” or “it’s not period wise” cause there are bigger issues than that and in like in 99,9% of things there is no real reason why should they not be cast.

EDIT: And, by the way, there are history books, lessons, documentaries and THE WHOLE net if you want to taste some historical truth.