1, 4, 9, 16, 15, 36,,, are called square numbers and they satisfy:
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16
5 * 5 = 25
6 * 6 = 36
and when odd numbers are added in good order, then they shall have the below property:
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
1 + 3 + 5 + 7 + 9 + 11 = 36
Pythagoras, the great votary of science of ancient Greece, proved the property by using the below diagram:
Nowadays, a high school student proves it by using numerical sequence.
[Personal Opinion]
Humans developed over centuries first by walking in erect posture, using words and then counting numbers. After the invention of numeric to count numbers, Pythagoras discovered that "numeric has the property" of being square numbers when "odd numbers are added." I believe it was a great discovery for humans at that time.
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