Amazing Number Circle
Below we will consider a few numbers arranged in a circle. The numbers are first 32 natural numbers, i.e., 1, 2, 3, . . . , 31, 32. The numbers on the circle are so arranged that the sum of any two consecutive numbers is a perfect square. While adding two consecutive numbers, either we get 9 = 32 or 16 = 42 or 25 = 52 or 36 = 62 or 49 = 72.
21 + 4 = 25 = 52
4 + 32 = 36 = 62
32 + 17 = 49 = 72
17 + 19 = 36 = 62
19 + 30 = 49 = 72
30 + 6 = 36 = 62
6 + 3 = 9 = 32
3 + 13 = 16 = 42
13 + 12 = 25 = 52
12 + 24 = 36 = 62
24 + 25 = 49 = 72
25 + 11 = 36 = 62
11 + 5 = 16 = 42
5 + 31 = 36 = 62
31 + 18 = 49 = 72
18 + 7 = 25 = 52
7 + 29 = 36 = 62
29 + 20 = 49 = 72
20 + 16 = 36 = 62
16 + 9 = 25 = 52
9 + 27 = 36 = 62
27 + 22 = 49 = 72
22 + 14 = 36 = 62
14 + 2 = 16 = 42
2 + 23 = 25 = 52
23 + 26 = 49 = 72
26 + 10 = 36 = 62
10 + 15 = 25 = 52
15 + 1 = 16 = 42
1 + 8 = 9 = 32
8 + 28 = 36 = 62
28 + 21 = 49 = 72
Numbers are beautiful!
Very interesting sir.
Thank you Sir
37 itself is interesting, and so are 37037, 37037037, etc. for similar reasons.
These are in pipeline. Thank you for your suggestion.
Wow…like this we can create more square numbers!!
Thank you Sourav.
Wow! Next time around, it’s Math for me!
Good to hear this. Thank you so much.
There is definately a great deal to learn about this subject. I really like all the points you’ve made.
Thank You