"The significant problems we have cannot be solved at the same level of thinking with which we created them." Albert Einstein

Monday, December 14, 2009

Math: The quadratic saga - Ep. 1 (My first post!)

Hi. Recently I was doing history homework when I remembered that when I was in sixth or seventh grade, a friend of mine and I squared the first numbers in order, and saw that the difference between one squared number and its previous would increase algebraically:



2² - 1²  =        4-1= 3
3² - 2² = 9-4 = 5
4² - 3² = 16 - 9 = 7
5² - 4² = 25 - 16 = 9
etc...


But since we were still little kids that didn't know anything about functions, we didn't even realize that the data that was just collected could give birth to a formula. In that day, while I was supposed to do the history homework, I remembered about it and realized that it wouldn't be difficult to make a formula that would relate a squared number and its previous squared number. In a few moments I related:

n² = (n-1)² + [2(n-1)+1]


And that day I stopped. I was already satisfied that I found the formula that I was looking for.


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