Definition:Pascal's Triangle/Historical Note

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 B.C.E. by the Hindu writer.


 * The earliest known detailed discussion on it was by in his Mṛtasañjīvanī from around $1000$ C.E. This was a commentary on 's Chandaḥ-sūtra, in which it was referred to as meru-prastaara.


 * In Iran it is known as the Khayyam Triangle after discussed it in ca. $1100$ C.E. It had been discussed even before that by  a hundred years previously.


 * In India it was discussed at length by in his ca. $1150$ work Līlāvatī.


 * In China it is known as Yang Hui's Triangle after, who himself (in $1261$) credited it to in a work (ca. $1000$ C.E.) now lost.


 * It also appears in 's, published in $1303$.


 * 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 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.


 * It is also known (particularly in Italy) as Tartaglia's Triangle, after.


 * It was used by, and  to calculate binomial coefficients.  in particular used it to calculate the coefficients of the expansion of the $12$th power.


 * It was 's $1665$ treatise (written in $1653$) which was perhaps the first time the main properties of this triangle were documented in one place.


 * The name Pascal's Triangle was assigned by in $1708$, and  in $1730$.