# Math - Hanna Young For my research paper, I chose the topic...

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Hanna Young For my research paper, I chose the topic of the numbers of squares in a square. I found a general formula by finding the amount of squares in each square based on its dimensions. After finding a general formula, I proved the formula by doing induction. The first step in the process of induction was making an N and T chart for the number of squares in the dimensional square. The N side is the sums while the T side is the terms. The first squares dimensions were a 1x1 which contained only 1 square for the terms side. The second square which had a dimension of 2x2 contained 4 1x1 squares and 1 2x2 square. The third square’s dimensions were 3x3 and contained 9 1x1 squares, 4 2x2 squares and 1 3x3 square. The fourth square contained 16 1x1 squares, 9 2x2 squares, 4 3x3 squares and 1 4x4 square. The fifth square contained 25 1x1 squares, 16 2x2 squares, 9 3x3 squares, 4 4x4 squares, and 1 5x5 square. The final square contained 36 1x1 squares, 25 2x2 squares, 16 3x3 squares, 9 4x4 squares, 4 5x5 squares and 1 6x6 square. After finding out the number of squares in each of the larger squares, I plugged in the answers to the chart. I then found the difference between the 1 st and 2 nd number, the 2 nd and 3 rd number, the 3 rd and 4 th number, the 4 th and 5 th number and the 5 th and 6 th

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number. Then I got smaller numbers and found the difference between those
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## This note was uploaded on 04/07/2011 for the course ASDASD asd taught by Professor Danseyar during the Spring '11 term at Quinnipiac.

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Math - Hanna Young For my research paper, I chose the topic...

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