Comments on: Surprising Patterns in the Square Numbers (1, 4, 9, 16…) https://betterexplained.com/articles/surprising-patterns-in-the-square-numbers-1-4-9-16/ Math lessons that click Mon, 03 Aug 2020 23:02:04 +0000 hourly 1 By: Nicolás Bonoris https://betterexplained.com/articles/surprising-patterns-in-the-square-numbers-1-4-9-16/#comment-567926 Mon, 03 Aug 2020 23:02:04 +0000 http://betterexplained.com/?p=914#comment-567926 In reply to kalid.

Thank you! It’s something I’m really liking so far.

]]> By: Nicolás Bonoris https://betterexplained.com/articles/surprising-patterns-in-the-square-numbers-1-4-9-16/#comment-567925 Mon, 03 Aug 2020 22:51:55 +0000 http://betterexplained.com/?p=914#comment-567925 In reply to geekybandit.

That’s wonderful. It’s crazy see numbers make that suspicious patterns sometimes.

]]> By: kalid https://betterexplained.com/articles/surprising-patterns-in-the-square-numbers-1-4-9-16/#comment-567924 Mon, 03 Aug 2020 22:16:56 +0000 http://betterexplained.com/?p=914#comment-567924 In reply to Nicolás Bonoris.

Hi Nicolas, that’s great to hear you were interested in pursuing your own research. A lot of interesting math results came from noticing new patterns.

]]> By: Nicolás Bonoris https://betterexplained.com/articles/surprising-patterns-in-the-square-numbers-1-4-9-16/#comment-567922 Sat, 01 Aug 2020 22:10:42 +0000 http://betterexplained.com/?p=914#comment-567922 I don´t know if it’s possible, but I found this properties of square numbers some time ago and I’m trying to make a formula to calculate square roots (and maybe cube and beyond).
The most surprising thing I found is that if you sum every digit of every square number, you’ll get a succession. But I´m stuck here, I don´t know how to proceed yet (my mathematical background is very lacking). Here you got the succession:
1=1
4=4
9=9
16=1+6=7
25=2+5=7
36=9
49=4
64=10=1
81=9
100=1
121=4
144=9
169=7
196=7
225=9
256=4
289=1
324=9

The patron of numbers (149779419149779419) then starts repeating.
I also saw in the succession that there are two groups of numbers that when finished are mirrored: 1497 *mirror 7941 – 91497 *mirror 79419.
This principle of summing the digits also applies to the Fibonacci sequence, that continues following the same rules when you do the same process.

Maybe it has no real mathematical relevance, but at least it’s really interesting, here are some really good ideas!

]]>