Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1, 1 + 2 + 1, 1 + 2 + 3 + 2 + 1, …, gives square numbers?

Pictorial explanation for adding Counting Numbers up and down to get square numbers:
The idea is to visualise each term in the sequence as rows of dots, where the sum
1 + 2 + 3 + 2 + 1 can be arranged as a perfect square. For example,
1 + 2 + 1 forms a 2 x 2 square,
1 + 2 + 3 + 2 + 1 forms a 3 x 3 square, and so on. Each layer of dots forms the next square by adding a symmetrical layer of dots around the existing square.

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