Jamshid al-Kashi

Jamshid al-Kashi was a 15th-century Persian mathematician and astronomer whose precise decimal arithmetic and trigonometric calculations advanced mathematical astronomy.

Sexagesimal system: A positional numeral system based on sixty, used historically in astronomy and timekeeping. Al-Kashi adapted inherited base-sixty astronomical practice while promoting decimal computation.
Law of cosines: A formula relating the lengths of a triangle’s sides to the cosine of one of its angles. Al-Kashi gave a general form of this relation that became known in Persian tradition by his name.
Timurid Empire: A Central Asian and Persianate empire founded by Timur and ruled by his successors from the late 14th century. Al-Kashi worked under Timurid patronage during a period of intense court scholarship.
Zij-i Sultani: An extensive astronomical handbook and star catalogue produced by Ulugh Beg’s Samarkand school. Al-Kashi helped prepare the computational foundations for this major astronomical work.
Decimal fractions: Fractions expressed in a positional decimal notation, allowing digits to represent tenths, hundredths, and smaller powers of ten. His systematic treatment helped establish decimal fractions as practical tools for calculation.
Al-Kashi's method: An iterative procedure for approximating roots of equations by successive numerical corrections. He used a root-finding approach to calculate the sine of one degree with high precision.
Ulugh Beg: A Timurid ruler and astronomer who established a major observatory and scholarly center in Samarkand. Ulugh Beg invited Al-Kashi to join the mathematical and astronomical community he assembled.
Astronomical tables: Collections of calculated values used to predict celestial positions and solve astronomical problems. His precision calculations contributed to the tables produced by the Samarkand school.
Numerical analysis: The study of algorithms for obtaining approximate numerical solutions to mathematical problems. His iterative calculations exemplify numerical methods developed before modern analysis.
Sine table: A tabulation of sine values for specified angles, used to solve geometric and astronomical problems. His tables supplied the numerical trigonometry required for detailed astronomical calculations.

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