And old indeed it was,for it was knowN in chinA BY 1100.The mathematician Chia Hsien expounded it at that time as 'the tabulation system for unlocking binomial coefficients'; but its first appearance is thought to have been in a book of that date, now lost, entitled Piling-up Powers and Unlocking Coefficients, by Liu Ju-Hsieh.

  The mathematician and poet Omar Khayyam discussed the Pascal Triangle somewhat indirectly about I 100. We do not know whether he got it from China or invented the elements of the system independently. But the first appearance of the Triangle in print in Europe was on the title page of the book on arithmetic of Petrus Apianus in 1527. Several succeeding mathematicians, such as Michael Stifel, considered it. And the Italian Nicolo Tartaglia, who was something of a scoundrel, claimed it as his own invention. But as far as we know, the inventor was indeed Liu Ju-Hsich, 427 years before the appearance of the 'Pascal' Triangle in Europe.

'Pascal's' Triangle was not invented by Blaise Pascal in 1654: it came from China. This diagram comes from Chu Shih-Chieh's Precious Mirror of the Four Elements, published in 1303. The caption refers to the triangle as the 'Old Method'; it had been expounded by the year I 100 by the mathematician Chia Hsien, who called it 'the tabulation system for unlocking binomial coefficients'.