Pascal's Triangle

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Algebra 2 Algebra 2 Pascal Investigation (5.7) 1. Who was Blaise Pascal (history)? Blaise Pascal, famous mathematician, was born in 1623 on June 19th, at Clermont. His father moved the family to Paris in the year 1631 to conduct his own scientific investigation as well as to pass on his knowledge to him only son. At first, young Pascal’s education did involve mathematics, only the study of languages. Pascal decided to learn about geometry, a topic he had only heard of but never studied, in his spare time. By age thirteen, he had proven the 32nd proposition of Euclid and discovered an error in Rene Descartes geometry. His father put Pascal’s knowledge in mathematics towards hand totaling long columns of numbers to his job. Pascal later went on the create the pascaline, a device fourteen by five by three inches that could do calculations, which can now be considered the first mechanical calculator. In 1650, Pascal suddenly decided to avidly study religion, but returned to his previous lifestyle three years later, conducting experiments on the pressure exerted by gases and liquids, inventing the arithmetical triangle, and created the calculus of probabilities together with Fermat. In 1654, Pascal abandoned the world after an accident and moved to Port Royal, where he lived until his death in 1662. 2. Who discovered Pascal’s Triangle? Pascal’s Triangle has been seen as early as 1261 in Chinese texts, attributing the triangle to a man that lived in the eleventh century named Jia Xian. 3. Discuss what it’s used for (3 applications used in algebra) & name and explain three patterns (1 algebraic) Pascal’s Triangle has various uses within algebra. For example, Pascal’s Triangle can be used to find out how many combinations of the two faces of a coin will result from x number of tosses. The number of tosses tells you which row to look at in the

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