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29 May 2009, 21:51
Kudos
Bookmarks
I'm not surew why I just now noticed this, but if you take the progression of perfect squares, you can find the next one by adding the next odd integer to the current perfect square, starting with adding 1 to 0 since 0 is technically the first perfect square.
0 (+1)
1 (+3)
4 (+5)
9 (+7)
16 (+9)
25 (+11)
36 (+13)
49 (+15)
64 (+17)
81 (+19)
100 (+21)
121
You see how the difference in the perfect squares is a pattern?
I have no idea what significance this has, but maybe someone out there with a deeper level of mathematics theory can shed some light on this, as well as explain whether this has any significance.
0 (+1)
1 (+3)
4 (+5)
9 (+7)
16 (+9)
25 (+11)
36 (+13)
49 (+15)
64 (+17)
81 (+19)
100 (+21)
121
You see how the difference in the perfect squares is a pattern?
I have no idea what significance this has, but maybe someone out there with a deeper level of mathematics theory can shed some light on this, as well as explain whether this has any significance.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
29 May 2009, 22:27
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jallenmorris
n , n+1 are consecutive integers
(n+1)^2 - n^2 = n^2 +1+2n -n^2 = 2n+1
So. For any perfect square n^2 to get the next perfect square, we need to add (2n+1).
n=10
n^2 =100
(n+1)^2 = 100 + (2n+1) = 100+(20+1) =121
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
