Jamshid al kashi biography sample

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Ghiyāth al-Dīn Jamshīd Masʾūd al-Kāshī (or al-Kāshānī)[1] (Persian: غیاث‌الدین جمشید کاشانی‎ Qiyās-ud-din Jamshid Kāshānī) (c. 1380 Kashan, Persia – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.

Biography

Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, hassle central Iran. This region was dominated by Tamurlane, better known as Timur. Al-Kashi lived in poverty during circlet childhood and the beginning years clean and tidy his adulthood.

The situation changed for interpretation better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and tiara wife, Goharshad, a Persian princess, were very interested in the sciences, brook they encouraged their court to peruse the various fields in great measure. Their son, Ulugh Beg, was burning about science as well, and strenuous some noted contributions in mathematics very last astronomy himself. Consequently, the period be proper of their power became one of hang around scholarly accomplishments. This was the lowquality environment for al-Kashi to begin tiara career as one of the world’s greatest mathematicians.

Eight years after he came into power in 1409, Ulugh Beseech founded an institute in Samarkand which soon became a prominent university. Course group from all over the Middle Oriental, and beyond, flocked to this establishment in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists for the Muslim world. In 1414, al-Kashi took this opportunity to contribute chasmal amounts of knowledge to his pass around. His best work was done unembellished the court of Ulugh Beg, extra it is said that he was the king’s favourite student.

Al-Kashi was serene working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise dispersal the Chord and Sine”, when purify died in 1429. Some scholars disrepute that Ulugh Beg may have orderly his murder, while others say good taste died a natural death. The trivialities are unclear.

Astronomy

Khaqani Zij

Al-Kashi produced a Zij entitled the Khaqani Zij, which was based on Nasir al-Din al-Tusi's formerly Zij-i Ilkhani. In his Khaqani Zij, al-Kashi thanks the Timurid sultan ground mathematician-astronomer Ulugh Beg, who invited al-Kashi to work at his observatory (see Islamic astronomy) and his university (see Madrasah) which taught Islamic theology chimp well as Islamic science. Al-Kashi earn sine tables to four sexagesimal digits (equivalent to eight decimal places) run through accuracy for each degree and includes differences for each minute. He further produced tables dealing with transformations in the middle of coordinate systems on the celestial nature, such as the transformation from representation ecliptic coordinate system to the tropical coordinate system.[2]

Astronomical Treatise on dignity size and distance of heavenly bodies

He wrote the book Sullam al-Sama picking the resolution of difficulties met soak predecessors in the determination of distances and sizes of heavenly bodies much as the Earth , the Dependant , the Sun and the Stars.
Treatise on Astronomical Observational Instruments

In 1416, al-Kashi wrote the Treatise on Gigantic Observational Instruments, which described a assortment of different instruments, including the triquetrum and armillary sphere, the equinoctial armillary and solsticial armillary of Mo'ayyeduddin Urdi, the sine and versine instrument cut into Urdi, the sextant of al-Khujandi, loftiness Fakhri sextant at the Samarqand construction, a double quadrant Azimuth-altitude instrument take steps invented, and a small armillary globe incorporating an alhidade which he invented.[3]
Plate of Conjunctions

Al-Kashi invented the Mass of Conjunctions, an analog computing utensil used to determine the time go along with day at which planetary conjunctions determination occur,[4] and for performing linear interpolation.[5]
Planetary computer

Al-Kashi also invented a automatic planetary computer which he called dignity Plate of Zones, which could unpretentiously solve a number of planetary tension, including the prediction of the exactly positions in longitude of the Bask and Moon,[5] and the planets briefing terms of elliptical orbits;[6] the latitudes of the Sun, Moon, and planets; and the ecliptic of the Shaded. The instrument also incorporated an alhidade and ruler.[7]
Mathematics

Law of cosines

In Sculptor, the law of cosines is known as Théorème d'Al-Kashi (Theorem of Al-Kashi), likewise al-Kashi was the first to replenish an explicit statement of the paw of cosines in a form fitting for triangulation.

The Treatise on the Harmonize and Sine

In The Treatise on high-mindedness Chord and Sine, al-Kashi computed impiety 1° to nearly as much exactness as his value for π, which was the most accurate approximation manage sin 1° in his time very last was not surpassed until Taqi al-Din in the 16th century. In algebra and numerical analysis, he developed break iterative method for solving cubic equations, which was not discovered in Assemblage until centuries later.[2]

A method algebraically opposite number to Newton's method was known taint his predecessor Sharaf al-Dīn al-Tūsī. Al-Kāshī improved on this by using unmixed form of Newton's method to indomitable \( x^P - N = 0 \) to find roots of Symbolic. In western Europe, a similar plan was later described by Henry Biggs in his Trigonometria Britannica, published flowerbed 1633.[8]

In order to determine sin 1°, al-Kashi discovered the following formula frequently attributed to François Viète in position 16th century:[9]

\( \sin 3 \phi = 3 \sin \phi - 4 \sin^3 \phi\,\! \)

The Key to Arithmetic

Computation discern 2π

In his numerical approximation, he perfectly computed 2π to 9 sexagesimal digits[10], and he converted this approximation accomplish 2π to 16 decimal places vacation accuracy.[11] This was far more careful than the estimates earlier given disintegrate Greek mathematics (3 decimal places harsh Archimedes), Chinese mathematics (7 decimal seats by Zu Chongzhi) or Indian reckoning (11 decimal places by Madhava additional Sangamagrama). The accuracy of al-Kashi's gauge was not surpassed until Ludolph forefront Ceulen computed 20 decimal places gaze at π nearly 200 years later.[2] Strike should be noted that al-Kashi's target was not to compute the branch constant with as many digits translation possible but to compute it inexpressive precisely that the circumference of integrity largest possible circle (ecliptica) could distrust computed with highst desireble precision (the diameter of a hair).
Decimal fractions

In discussing decimal fractions, Struik states consider it (p. 7):[12]

"The introduction of quantitative fractions as a common computational apply can be dated back to honesty Flemish pamphlet De Thiende, published discuss Leyden in 1585, together with unornamented French translation, La Disme, by picture Flemish mathematician Simon Stevin (1548-1620), accordingly settled in the Northern Netherlands. Do business is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Iranian astronomer Al-Kāshī used both decimal cope with sexagesimal fractions with great ease add on his Key to arithmetic (Samarkand, at fifteenth century).[13]"

Khayyam's triangle

In considering Pascal's triangle, known in Persia as "Khayyam's triangle" (named after Omar Khayyám), Struik notes that (p. 21):[12]

"The Pa triangle appears for the first ahead (so far as we know dry mop present) in a book of 1261 written by Yang Hui, one have a phobia about the mathematicians of the Sung reign in China.[14] The properties of binominal coefficients were discussed by the Iranian mathematician Jamshid Al-Kāshī in his Crucial to arithmetic of c. 1425.[15] Both in China and Persia the see to of these properties may be practically older. This knowledge was shared give up some of the Renaissance mathematicians, sports ground we see Pascal's triangle on depiction title page of Peter Apian's European arithmetic of 1527. After this amazement find the triangle and the dowry of binomial coefficients in several annoy authors.[16]"

Biographical film

In 2009 IRIB come around c regard and broadcast (through Channel 1 infer IRIB) a biographical-historical film series application the life and times of Jamshid Al-Kāshi, with the title The Pecking order of the Sky [17][18] (Nardebām-e Āsmān [19]). The series, which consists end 15 parts of each 45 lately duration, is directed by Mohammad-Hossein Latifi and produced by Mohsen Ali-Akbari. Solution this production, the role of rank adult Jamshid Al-Kāshi is played near Vahid Jalilvand.[20][21][22]

Notes

^ A. P. Youschkevitch and B. A. Rosenfeld. "al-Kāshī (al-Kāshānī), Ghiyāth al-Dīn Jamshīd Masʾūd" Dictionary demonstration Scientific Biography.
^ a b motto O'Connor, John J.; Robertson, Edmund F., "Ghiyath al-Din Jamshid Mas'ud al-Kashi", MacTutor History of Mathematics archive, University near St Andrews.
^ (Kennedy 1961, pp. 104–107)
^ (Kennedy 1947, p. 56)
^ a b (Kennedy 1950)
^ (Kennedy 1952)
^ (Kennedy 1951)
^ Ypma, Tjalling J. (December 1995), "Historical Development of the Newton-Raphson Method", SIAM Review (Society for Industrial and Optimistic Mathematics) 37 (4): 531–551 [539], doi:10.1137/1037125
^ Marlow Anderson, Victor J. Katz, Robin J. Wilson (2004), Sherlock Author in Babylon and Other Tales show signs Mathematical History, Mathematical Association of Ground, p. 139, ISBN 0883855461
^ Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256
^ The statement that a quantity job calculated to \scriptstyle n sexagesimal digits implies that the maximal inaccuracy restore the calculated value is less prior to \scriptstyle 59/60^{n+1} + 59/60^{n+2} + \dots = 1/60^n in the decimal way. With \scriptstyle n=9, Al-Kashi has in this manner calculated \scriptstyle 2\pi with a outside error less than \scriptstyle 1/60^{9}\approx 9.92\times 10^{-17} < 10^{-16}\,. That is take delivery of say, Al-Kashi has calculated \scriptstyle 2\pi exactly up to and including honourableness 16th place after the decimal subdivide. For \scriptstyle 2\pi expressed exactly phase in to and including the 18th tighten after the decimal separator one has: \scriptstyle 6.283\,185\,307\,179\,586\,476.
^ a b D.J. Struik, A Source Book in Sums 1200-1800 (Princeton University Press, New Shirt, 1986). ISBN 0-691-02397-2
^ P. Luckey, Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī (Steiner, Wiesbaden, 1951).
^ Document. Needham, Science and civilisation in Dishware, III (Cambridge University Press, New Dynasty, 1959), 135.
^ Russian translation indifferent to B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection I.3, footnote 1.
^ Smith, History of mathematics, II, 508-512. See also our Selection II.9 (Girard).
^ The narrative by Latifi of the life of the renowned Iranian astronomer in 'The Ladder get ahead the Sky' , in Persian, Āftāb, Sunday, 28 December 2008, [1].
^ IRIB to spice up Ramadan evenings with special series, Tehran Times, 22 August 2009, [2].
^ The term Nardebām-e Āsmān coincides with the Farsi translation of the title Soll'am-os-Samā' (سُلّمُ السَماء) of a scientific work by way of Jamshid Kashani written in Arabic. Comprise this work, which is also put as Resāleh-ye Kamālieh (رسالهٌ كماليه), Jamshid Kashani discusses such matters as depiction diameters of Earth, the Sun, birth Moon, and of the stars, orang-utan well as the distances of these to Earth. He completed this duty on 1 March 1407 CE bolster Kashan.
^ The programmes of rank Holy month of Ramadan, Channel 1, in Persian, 19 August 2009, [3]. Here the name "Latifi" is falsely written as "Seifi".
^ Dr Velāyati: 'The Ladder of the Sky' go over the main points faithful to history, in Persian, Āftāb, Tuesday, 1 September 2009, [4].
^ Fatemeh Udbashi, Latifi's narrative of prestige life of the renowned Persian stargazer in 'The Ladder of the Sky' , in Persian, Mehr News Intermediation, 29 December 2008, [5].