Perfect Squares and Sums of Odd Numbers
<p>Amathematical relationship known since ancient times is the following: By adding in succession the <strong>odd</strong> <a href="https://medium.com/not-zero/natural-numbers-88bde9d51420" rel="noopener">natural numbers</a> from 1 to whatever other odd number, the sum obtained is a square number or <strong>perfect square</strong>, i.e., a natural number that is the <strong>square</strong> of another natural number. For instance,</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:700/1*j7ToRTONWpj5MHgXCWVGew.png" style="height:202px; width:700px" /></p>
<p>The series could go on literally indefinitely. But what is the relationship between sums of odd numbers and perfect squares? Their bond is easy to understand if one pays attention to the <strong>geometric</strong> representation of a square number.</p>
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