Pascal's Birthday

Pascal's Triangle carries significance throughout the history that it has been used in various ways. One of these main ways that the Pascal's Triangle is used is by foiling. For example,


This method of the Pascal Triangle is used basically as a short cut to understanding how to foil more complex polynomial factoring. This works by having the exponent of the quadratic equation match the row in the Pascal triangle. There are many more ways that the Pascal Triangle has been useful, one of these ways is by finding the power of 11. In this instance 11 to the power of 4 matches the fourth row in the Pascal Triangle! But when the power of 11 is changed to 7, we find that the answer is 17213535 2171? 11 to the power of 7 is 19487171. In order to solve this we take the tens place of each number in the 7th row in the triangle and add them to the ones place to the number from right to left


1 7 21 35 35 21 7 1= eigth digit 1
seventh digit 7
sixth digit 1
fifth digit 2+5=7
fourth digit 3+5= 8
third digit 3+1= 4
second digit 2+7=9
first digit 1

11 to the power of 7 is 19487171

Here's also two types of Pascal's triangles;

                                                                    Pascal

                                                          Pascal            Pascal

                                                 Pascal         Pascal      Pascal              

                                       Pascal        Pascal          Pascal      Pascal

                            Pascal         Pascal       Pascal           Pascal      Pascal 

                 Pascal          Pascal         Pascal       Pascal           Pascal   Pascal                                        Pascal        Pascal         Pascal         Pascal        Pascal          Pascal         Pascal