Math exploration of Pascals Triangle Essay Example | Topics and Well Written Essays - 1750 words

Math exploration of Pascals Triangle - Essay Example As a mathematics student and an astronomer, he made immense contributions to the revision of the Chongtian calendar in 1023 while he also served in the Imperial Astronomical Bureau in the middle of the 11th century. However, he is mostly remembered because he devised a method of extracting the solutions of solutions of degrees higher than three extracts. The method is as to the Chia-Hsien triangle which contains binomial coefficients of binomial expressions up to the sixth degree. This triangle is similar to the Pascal’s triangle that was later discovered in Europe. In India, the expansion of binomial expressions was not well researched and studied. However, Brahmagupta in 628 A.D correctly expanded (a + b )3. It was one level higher that what Eucid, a Greek mathematician, did. Although his work may not be the greatest, it found its way to Baghdad after several decades and elicited some curiosity about binomial coefficients amongst mathematicians in the Middle East (Bassarear, pp178-212) Amongst those who used the work of Brahmagupta as a basis of more research in the Middle East is Al-Din Al-Tusi. Al-Din Al-Tusi works were published in 1265 and Al-Kashi whose work titled â€Å"Key of Arithmetic† contained the triangle up to the ninth degree. In Europe, several authors discussed ideas with respect to expansion of binomials and combinatorial problems (Cullinane, pp.145-178). A Spanish mathematician, Rabbi Ben Ezra in 1140 discovered the seventh row of the Pascal’s triangle. Moreover, this was in relation to the question of taking into consideration the sun and the corresponding six planets, which were known at that time in combinations of a single element each period, which is repeated each time. Fibonacci in 122 independently wrote down the solutions of the binomial equation of the third degree although it was known in India and Middle East (Birken & Anne, pp.124-167). Fibonacci was also the first European