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The earliest explicit depictions of a triangle of [[binomial coefficients]] occur in the [[10th century]] in a commentary on the ''Chandas Shastra'', an [[ancient India]]n book on [[Sanskrit]] [[prosody]] written by [[Pingala]] between the [[5th century BC|5th]]–[[2nd century BC|2nd centuries BC]]. While Pingala's work only survives in fragments, the commentator [[Halayudha]], around [[975]], used the triangle to explain obscure references to ''Meru-prastaara'', the "Staircase of [[Mount Meru]]". It was also realised that the shallow diagonals of the triangle sum to the [[Fibonacci numbers]]. The [[Indian mathematics|Indian mathematician]] Bhattotpala (c. [[1068]] later gives rows 0-16 of the triangle.
[[Image:Yanghui_triangle.gif|thumb|left|[[Yang Hui]] (Pascal's) triangle, as depicted by the Chinese using [[Counting rods|rod numerals]].]]
At around the same time, it was discussed in [[History of Iran|Persia]] by the [[Islamic mathematics|mathematician]] [[Al-Karaji]] (953–1029) and the [[Persian literature|poet]]-[[Islamic astronomy|astronomer]]-mathematician [[Omar Khayyám]] (1048-1131); thus the triangle is referred to as the "Khayyam triangle" in [[Iran]]. Several theorems related to the triangle were known, including the [[binomial theorem]]. In fact we can be fairly sure that Khayyam used a method of finding ''n''th roots based on the binomial expansion, and therefore on the binomial coefficients.
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