Definition:Pascal's Triangle/Historical Note

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Historical Note on Pascal's Triangle

  • The earliest reference to Pascal's triangle seems to date from between the $5$th and $2$nd centuries BCE by the Hindu writer Pingala.
  • The earliest known detailed discussion on it was by Halayudha in his Mṛtasañjīvanī from around $1000$ CE. This was a commentary on Pingala's Chandaḥ-sūtra, in which it was referred to as meru-prastaara.
  • While the binomial coefficients for small arguments appear in works of the ancient Greeks and Romans, the first actual record of Pascal's triangle in Europe seems to be when Petrus Apianus published it on the frontispiece of his $1527$ book on business calculations Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen.