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# An analysis of Pascal's Triangle in Mathematics

Pascals TriangleBlas Pacal was born in France in 1623 He was a child prodigy and wasfascinated by mathematics When Pascal was 19 he invented the first calculatingmachine that actually worked Many other people had tried to do the same but did notsucceed One of the topics that deeply interested him was the likelihood of an eventhappening probability This interest came to Pascal from a gambler who asked himto help him make a better guess so he could make an educated guess In the coarse ofhis investigations he produced a triangular pattern that is named after him The patternwas known at least three hundred years before Pascal had discover it The Chinesewere the first to discover it but it was fully developed by Pascal Ladja 2Pascals triangle is a triangluar arrangement of rows Each row except the firstrow begins and ends with the number 1 written diagonally The first row only has onenumber which is 1 Beginning with the second row each number is the sum of thenumber written just above it to the right and the left The numbers are placed midwaybetween the numbers of the row directly above itIf you flip 1 coin the possibilities are 1 heads H or 1 tails T Thiscombination of 1 and 1 is the firs row of Pascals Triangle If you flip the coin twiceyou will get a few different results as I will show below Ladja 3 Lets say you have the polynomial x1 and you want to raise it to some powers like 12345 If you make a chart of what you get when you do these power-raisins youll get something like this Dr Math 3 x10 1 x11

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