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153 lines
4.7 KiB
HTML
153 lines
4.7 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/numbers/odd-square-number.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:45:41 GMT -->
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<head>
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<title>Squares and Odd Numbers</title>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Squares and Odd Numbers</h1>
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<p>Add up odd numbers from 1 onwards and you get <a href="../square-root.html">square numbers</a>!</p>
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<ul>
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<li><b>1</b> is a square number (= 1 × 1)</li>
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<li>1 + 3 = <b>4</b>, and 4 is a square number (= 2 × 2)</li>
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<li>1 + 3 + 5 = <b>9</b>, and 9 is a square number (= 3 × 3)</li>
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<li>etc!</li>
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</ul>
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<p>Like this:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tr style="text-align:center;">
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<th>Odd<br>
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Number</th>
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<th>Running<br>
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Total</th>
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<th> </th>
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</tr>
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<tr style="text-align:center;">
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<td>1</td>
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<td>1</td>
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<td>= 1 × 1</td>
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</tr>
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<tr style="text-align:center;">
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<td>3</td>
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<td>4</td>
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<td>= 2 × 2</td>
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</tr>
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<tr style="text-align:center;">
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<td>5</td>
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<td>9</td>
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<td>= 3 ×3</td>
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</tr>
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<tr style="text-align:center;">
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<td>7</td>
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<td>16</td>
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<td>= 4 × 4</td>
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</tr>
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<tr style="text-align:center;">
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<td>9</td>
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<td>25</td>
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<td>= 5 × 5</td>
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</tr>
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<tr style="text-align:center;">
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<td>11</td>
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<td>36</td>
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<td>= 6 × 6</td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">etc...</td>
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</tr>
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</table>
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</div>
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<h3><i>Is this some kind of magic?</i></h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/odd-square-numbers.gif" width="156" height="130" alt="odd square numbers" /></p>
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<p>Not really, just look at this picture:</p>
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<ul>
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<li><b>1</b> is a square (a 1×1 square)</li>
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<li>Add <b>3</b> and you get a 2×2 square</li>
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<li>Add <b>5</b> and you get a 3×3 square</li>
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<li>etc</li>
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</ul>
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<p>It is good to know this, as it may help you solve things one day.</p>
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<p>There are more such tricks, see <a href="../algebra/partial-sums.html">Partial Sums</a>.</p>
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<p> </p>
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<div class="related">
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<a href="../square-root.html">Squares and Square Roots</a>
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<a href="index.html">Numbers Index</a>
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</div>
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Copyright © 2020 MathsIsFun.com
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