Tim

Phase One Yang Hui. == There is not much information about Yang Hui which he relates in his books. He tells us that he was taught by mathematics Liu Yi I who was a native of Chung-shan, in Kwangtung province, which is south of Chekiang province where Yang Hui was born. Nothing at all is known of Liu Yi, so this information is not beneficent in giving us details of Yang Hui. We know four of Yang's friends who were also interested in mathematics but these men are undisclosed except for Yang's reference to them. The best guess that historians make is that Yang was a insignifacant Chinese official. Most Chinese scholars of the period were officials, for there were no professional mathematicians, but he could not have held an important post since were he a major  official he would appear in records of the dynasty **//. People know him for his Magic Squares, Magic circles and his binomial theorem. He is best known for his work on Yang Hui's Triangle Yang Hui's Triangle is similar to Pascal's Triangle. Pascal's Triangle is an arrangement of//** **//binomial coefficients grouped into a triangle.//** The only existing work of Pascal's Triangle is from Yang's book //Xiangjie Jiuzhang Suanfa// of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian who founded it around 1100 AD, about 500 years before Pasca l.== http://en.wikipedia.org/wiki/Yang_Hui

== **//Yang Hui represents the quadratic equation//** with his negative coefficients of x become evident, although he attributes this to the earlier Liu Yi. In his written work, Yang provided theoretical proof for the proposition that the complements of the parallelograms which are about the diameter of any given parallelogram are equal to one another. ==

Abraham bar Hiyya

Abraham bar Hiyya is remembered in the world of math for his role in the dissemination of the quadratic equation. He wrote some scientific works in astronomy, math, land surveying and calculating the calendar. He also wrote two religious works in the field of Judaism and the Jewish Bible. Even these religious works contain scientific speculation.Bar Hiyya wrote all his works in Hebrew and not in Judea-Arabic of the earlier Jewish scientific literature, which made him one of the first guys to use the Hebrew Language for scientific reasons. He also cooperated with Plato Tivoli in the translation of scientific works from Arabic into Latin.

Abraham bar Ḥiyya, together with Abraham Ibn Ezra, holds an important place in the history of Jewish science. He was, indeed, one of the most important figures in the scientific movement which made the Jew of Province, Spain, and Italy the intermediaries between Mohammedan Science and the Christian world. http://en.wikipedia.org/wiki/Abraham_bar_Hiyya



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