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.
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Thank you Sir
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37 itself is interesting, and so are 37037, 37037037, etc. for similar reasons.
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These are in pipeline. Thank you for your suggestion.
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Wow…like this we can create more square numbers!!
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Thank you Sourav.
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Wow! Next time around, it’s Math for me!
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Good to hear this. Thank you so much.
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There is definately a great deal to learn about this subject. I really like all the points you’ve made.
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Thank You
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