# Perfect squares **URL:** \ **Category:** Factual Questions\ **Created:** [November 28, 2000, 9:30pm UTC](https://boards.straightdope.com/t/perfect-squares/43091 "2000-11-28T21:30:34Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [November 28, 2000, 9:30pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/1 "2000-11-28T21:30:34Z")
With time to kill at my job and attempting to look busy, I started writing out the squares of all the positive integers. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, got bored. Anyway, I noticed that when you go from 16 to 25, you add another perfect square (9), and when you go from to 144 to 169, you add another perfect square (25). Is there a pattern to this happening or does it just sort of show up every now and then? ---
**Author:** ![Friday](https://avatars.discourse-cdn.com/v4/letter/f/dec6dc/32.png) [@Friday](https://boards.straightdope.com/u/Friday)\ **Post date:** [November 28, 2000, 9:35pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/2 "2000-11-28T21:35:43Z")
Actually, the perfect squares you show is a pattern; you are adding the next odd integer to the previous. So you will get all the odd numbers squared eventually. ---
**Author:** ![LazarusLong42](https://avatars.discourse-cdn.com/v4/letter/l/87869e/32.png) [@LazarusLong42](https://boards.straightdope.com/u/LazarusLong42)\ **Post date:** [November 28, 2000, 9:39pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/3 "2000-11-28T21:39:59Z")
n^2 = SUM(2n-1) from 1 to n ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [November 28, 2000, 9:42pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/4 "2000-11-28T21:42:55Z")
Thank you. I received good grades in math all the way through integral calculus. However, I doubt I understood much of it. ---
**Author:** ![Saltire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saltire/32/553_2.png) [@Saltire](https://boards.straightdope.com/u/Saltire)\ **Post date:** [November 28, 2000, 10:18pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/5 "2000-11-28T22:18:59Z")
Not really any sort of answer, but I thought I’d point out that these triplets you’re finding are indications of unit right triangles. The roots of these squares are whole numbers that fit into a[sup]2[/sup]+b[sup]2[/sup]=c[sup]2[/sup](the Pythagoren theorem). So, the can form right triangles with whole number sides, like the famous 3-4-5 triangle. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 28, 2000, 11:00pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/6 "2000-11-28T23:00:14Z")
0[sup]2[/sup] and 1[sup]2[/sup] also differ by a perfect square. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [November 28, 2000, 11:01pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/7 "2000-11-28T23:01:45Z")
I knew about 0 and 1, but I hoped that I was specific enough by saying positive integers. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 28, 2000, 11:16pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/8 "2000-11-28T23:16:33Z")
Right you are. I should have paid closer attention. ---
**Author:** ![BobT](https://avatars.discourse-cdn.com/v4/letter/b/8e8cbc/32.png) [@BobT](https://boards.straightdope.com/u/BobT)\ **Post date:** [November 28, 2000, 11:28pm UTC](https://boards.straightdope.com/t/perfect-squares/43091/9 "2000-11-28T23:28:12Z")
Wow! I got a math thing right, sort of! I think I should stick to explaining the niceties of illegal touching on punts in football.