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!