L6 Central Limit Theorem

Read in the name of your Lord Who created. He created man from a clot. Read and your Lord is Most Honorable, Who taught (to write) with the pen. Taught man what he knew not. (Surah Al Alaq 96:1-5)

These are the first words of the wahi, revealed to the Prophet Mohammad SAW, when he was searching for the truth while meditating in the Cave of Hira. Allah Subhanahu wa T'aala introduces Himself as the Teacher -- as the first among the thousands of Characteristics and Names that He has. It was these revolutionary teachings which transformed the ignorant and backwards Muslims into world leaders. It is neglect of these teachings which has made us backwards today. Useful KNOWLEDGE is the key to success in this world and the herafter.

C1: Sums Are Normal

C2 CLT for Binomials

C3 CLT for Chi-Squares

C4 Survey Sampling Errors

C5 Simulations

Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī)^[1] (Persian: غیاث الدین جمشید کاشانی‎‎ Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer andmathematician.

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 systemson the celestial sphere, such as the transformation from the ecliptic coordinate system to the equatorial coordinate system.

Al-Kashi invented the Plate of Conjunctions, an analog computing instrument used to determine the time of day at whichplanetary conjunctions will occur,^[5] and for performing linear interpolation.^[6]

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 the Sun and Moon,^[6] and theplanets in terms of elliptical orbits;^[7] the latitudes of the Sun, Moon, and planets; and the ecliptic of the Sun. The instrument also incorporated an alhidade and ruler.^[8]

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. 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 was not discovered in Europe until centuries later.^[3]