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28-640: Ghiyath or Ghiyāth is a given name. Notable people with the name include: Ghiyath al-Kashi (1380–1429), Persian astronomer and mathematician Ghiyath al-Din Abu'l-Fath Omar ibn Ibrahim Al-Nisaburi Khayyami (1048–1131), Persian polymath: philosopher, mathematician, astronomer and poet Ghiyath ad-Din Mas'ud (1108–1152), the Seljuq Sultan of Iraq and western Persia Ghiyāth al-dīn Naqqāsh ( fl. 1419–22), envoy of

56-859: A French translation, La Disme , by the Flemish mathematician Simon Stevin (1548-1620), then settled in the Northern Netherlands . It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century). " In considering Pascal's triangle , known in Persia as "Khayyam's triangle" (named after Omar Khayyám ), Struik notes that (p. 21): "The Pascal triangle appears for

84-545: A prominent university. Students from all over the Middle East and beyond, flocked to this academy in the capital city of Ulugh Beg's empire. Consequently, Ulugh Beg gathered many great mathematicians and scientists of the Middle East . In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg. Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on

112-614: A variety of different instruments, including the triquetrum and armillary sphere , the equinoctial armillary and solsticial armillary of Mo'ayyeduddin Urdi , the sine and versine instrument of Urdi, the sextant of al-Khujandi , the Fakhri sextant at the Samarqand observatory, a double quadrant Azimuth - altitude instrument he invented, and a small armillary sphere incorporating an alhidade which he invented. Al-Kashi invented

140-545: Is al- Risāla al - muhītīyya or "The Treatise on the Circumference". In The Treatise on the Chord and Sine , al-Kashi computed sin 1° to nearly as much accuracy as his value for π , which was the most accurate approximation of sin 1° in his time and was not surpassed until Taqi al-Din in the sixteenth century. In algebra and numerical analysis , he developed an iterative method for solving cubic equations , which

168-475: The Renaissance mathematicians, and we see Pascal 's triangle on the title page of Peter Apian 's German arithmetic of 1527. After this, we find the triangle and the properties of binomial coefficients in several other authors. " In 2009, IRIB produced and broadcast (through Channel 1 of IRIB) a biographical-historical film series on the life and times of Jamshid Al-Kāshi, with the title The Ladder of

196-539: The Sun and Moon , and the planets in terms of elliptical orbits ; the latitudes of the Sun, Moon, and planets; and the ecliptic of the Sun. The instrument also incorporated an alhidade and ruler . In French , the law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines in a form suitable for triangulation . His other work

224-510: The Timurid sultan and mathematician-astronomer Ulugh Beg , who invited al-Kashi to work at his observatory (see Islamic astronomy ) and his university (see Madrasah ) which taught theology . Al-Kashi produced sine tables to four sexagesimal digits (equivalent to eight decimal places) of accuracy for each degree and includes differences for each minute. He also produced tables dealing with transformations between coordinate systems on

252-654: The celestial sphere , such as the transformation from the ecliptic coordinate system to the equatorial coordinate system . He wrote the book Sullam al-sama' on the resolution of difficulties met by predecessors in the determination of distances and sizes of heavenly bodies , such as the Earth , the Moon , the Sun , and the Stars . In 1416, al-Kashi wrote the Treatise on Astronomical Observational Instruments , which described

280-697: The lunar crescent , astronomical and/or astrological computations, and instructions for astronomical calculations using epicyclic geocentric models. Some zīj es go beyond this traditional content to explain or prove the theory or report the observations from which the tables were computed. Due to religious conflicts with astrology, many astronomers attempted to separate themselves from astrology, specifically intending for their zīj es not to be used for astrological computations. However, many zīj es were used this way regardless, such as ibn al-Shatir 's al-Zij al-jadīd . Over 200 different zīj es have been identified that were produced by Islamic astronomers during

308-501: The positions of the sun, moon, stars, and planets. The name zīj is derived from the Middle Persian term zih or zīg "cord". The term is believed to refer to the arrangement of threads in weaving, which was transferred to the arrangement of rows and columns in tabulated data. Some such books were referred to as qānūn , derived from the equivalent Greek word, κανών . The Zij-i Sultani , published by

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336-472: The sciences , and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world's greatest mathematicians. Eight years after he came into power in 1409, their son, Ulugh Beg , founded an institute in Samarkand which soon became

364-714: The "Handy Tables" by Ptolemy , known in Arabic as al-Qānūn , the Zīj-i Shāh compiled in Sasanian Persia, and the Indian siddhantas by Āryabhaṭa and Brahmagupta . Muslim zīj es, however, were more extensive, and typically included materials on chronology , geographical latitudes and longitudes , star tables, trigonometrical functions , functions in spherical astronomy , the equation of time , planetary motions, computation of eclipses , tables for first visibility of

392-527: The Chord and Sine”, when he died, in 1429. Some state that he was murdered and say that Ulugh Beg probably ordered this, whereas others suggest he died a natural death. Regardless, after his death, Ulugh Beg described him as "a remarkable scientist" who "could solve the most difficult problems". Al-Kashi produced a Zij entitled the Khaqani Zij , which was based on Nasir al-Din al-Tusi 's earlier Zij-i Ilkhani . In his Khaqani Zij , al-Kashi thanks

420-458: The Plate of Conjunctions, an analog computing instrument used to determine the time of day at which planetary conjunctions will occur, and for performing linear interpolation . Al-Kashi also invented a mechanical planetary computer which he called the Plate of Zones, which could graphically solve a number of planetary problems, including the prediction of the true positions in longitude of

448-566: The Sky ( Nardebām-e Āsmān ). The series, which consists of 15 parts, with each part being 45 minutes long, is directed by Mohammad Hossein Latifi and produced by Mohsen Ali-Akbari. In this production, the role of the adult Jamshid Al-Kāshi is played by Vahid Jalilvand. Zij A zij ( Persian : زيج , romanized :  zīj ) is an Islamic astronomical book that tabulates parameters used for astronomical calculations of

476-714: The Timurid ruler of Persia and Transoxania to China Ghiyath ad-Din Mehmed I Tapar (died 1118), son of Seljuq Sultan Malik Shah I Ghiyath al-Din Tughluq (died 1325), the founder and first ruler of the Muslim Tughluq dynasty See also [ edit ] Ghiyath al-Din (disambiguation) Ghiyas (disambiguation) (a different transcription of essentially the same name) Gaeth Goath [REDACTED] Name list This page or section lists people that share

504-470: The astronomer and sultan Ulugh Beg in 1438/9, was used as a reference zij throughout Islam during the early modern era . Omar Khayyam 's Zij-i Malik Shahi was updated throughout the modern era under various sultanates. Zijes were updated by different empires to suit their various interests, such as the simplified version of Zij-i Sultani by the Mughal Empire . Some of

532-750: The early zīj es tabulated data from Indian planetary theory (known as the Sindhind) and from pre-Islamic Sasanian models, but most zīj es presented data based on the Ptolemaic model . A small number of the zīj es adopted their computations reflecting original observations but most only adopted their tables to reflect the use of a different calendar or geographic longitude as the basis for computations. Since most zīj es generally followed earlier theory, their principal contributions reflected improved trigonometrical, computational and observational techniques. The content of zīj es were initially based on that of

560-558: The first time (so far as we know at present) in a book of 1261 written by Yang Hui , one of the mathematicians of the Song dynasty in China . The properties of binomial coefficients were discussed by the Persian mathematician Jamshid Al-Kāshī in his Key to arithmetic of c. 1425. Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of

588-503: The following formula, often attributed to François Viète in the sixteenth century: sin ⁡ 3 ϕ = 3 sin ⁡ ϕ − 4 sin 3 ⁡ ϕ {\displaystyle \sin 3\phi =3\sin \phi -4\sin ^{3}\phi \,\!} In his numerical approximation , he correctly computed 2 π to 9 sexagesimal digits in 1424, and he converted this estimate of 2 π to 16 decimal places of accuracy. This

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616-662: The most famous Indian zīj es was the Zīj-i Muhammad Shāhī , compiled at Sawai Jai Singh 's Jantar Mantar observatories in the Kingdom of Amber . It is notable for employing the use of telescopic observations. The last known zīj treatise was the Zīj-i Bahadurkhani , written in 1838 by the Indian astronomer Ghulam Hussain Jaunpuri (1760–1862) and printed in 1855, dedicated to Bahadur Khan . The treatise incorporated

644-658: The period from the eighth to the fifteenth centuries. The greatest centers of production of zīj es were Baghdad under the Abbasid caliphs in the ninth century, the Maragheh observatory in the 13th century, the Samarkand observatory in the 15th century, and the Constantinople observatory of Taqi ad-Din in the 16th century. Nearly 100 more zīj es were also produced in India between the 16th and 18th centuries. One of

672-465: The same given name . If an internal link led you here, you may wish to change that link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Ghiyath&oldid=1100118260 " Category : Given names Hidden categories: Articles with short description Short description is different from Wikidata All set index articles Ghiyath al-Kashi Much of al-Kāshī's work

700-481: Was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Ptolemy , AD 150), Chinese mathematics (7 decimal places by Zu Chongzhi , AD 480) or Indian mathematics (11 decimal places by Madhava of Kerala School , c. 14th Century ). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π 180 years later. Al-Kashi's goal

728-488: Was not brought to Europe and still, even the extant work, remains unpublished in any form. Al-Kashi was born in 1380, in Kashan , in central Iran, to a Persian family. This region was controlled by Tamerlane , better known as Timur. The situation changed for the better when Timur died in 1405, and his son, Shah Rokh , ascended into power. Shah Rokh and his wife, Goharshad , a Turkish princess, were very interested in

756-586: Was not discovered in Europe until centuries later. A method algebraically equivalent to Newton's method was known to his predecessor Sharaf al-Din al-Tusi . Al-Kāshī improved on this by using a form of Newton's method to solve x P − N = 0 {\displaystyle x^{P}-N=0} to find roots of N . In western Europe , a similar method was later described by Henry Briggs in his Trigonometria Britannica , published in 1633. In order to determine sin 1°, al-Kashi discovered

784-499: Was to compute the circle constant so precisely that the circumference of the largest possible circle (ecliptica) could be computed with the highest desirable precision (the diameter of a hair). In discussing decimal fractions , Struik states that (p. 7): "The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende , published at Leyden in 1585, together with

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