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jallenmorris
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Interesting Observation of Progression of Perfect Squares 29 May 2009, 21:51
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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.



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x2suresh
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Interesting Observation of Progression of Perfect Squares 29 May 2009, 22:27
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jallenmorris


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.

Show more

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



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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
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Thank you for understanding, and happy exploring!