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src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Rule_of_twelfths.svg/400px-Rule_of_twelfths.svg.png" decoding="async" width="400" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Rule_of_twelfths.svg/600px-Rule_of_twelfths.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Rule_of_twelfths.svg/800px-Rule_of_twelfths.svg.png 2x" data-file-width="512" data-file-height="279" /></a><figcaption>Graph showing relationships between the rule of twelfths (coloured bars), a sine wave (dashed blue curve) and a clockface, if high tide occurs at 12:00</figcaption></figure> <p>The <b>rule of twelfths</b> is an approximation to a <a href="/wiki/Sine_curve" class="mw-redirect" title="Sine curve">sine curve</a>. It can be used as a <a href="/wiki/Rule_of_thumb" title="Rule of thumb">rule of thumb</a> for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide or the change in day length over the seasons. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="The_rule">The rule</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=1" title="Edit section: The rule"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rule states that over the first period the quantity increases by 1/12. Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths. </p> <table class="wikitable"> <tbody><tr> <th rowspan="2">Period</th> <th rowspan="2">Rule or<br />actual<br />values </th> <th colspan="3">Increment</th> <th colspan="3">Cumulative </th></tr> <tr> <th>Exact value</th> <th>Decimal</th> <th>Relative size</th> <th>Exact value</th> <th>Decimal</th> <th>Relative size </th></tr> <tr> <th rowspan="2">1 </th> <td>Rule</td> <td>1 / 12</td> <td>0.08333 </td> <td align="left"><span style="display:none;">0.08333</span><div style="width:16.666px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>1 / 12</td> <td>0.08333 </td> <td align="left"><span style="display:none;">0.08333</span><div style="width:16.666px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 0° - cos 30°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 30°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">2 </th> <td>Rule</td> <td>2 / 12</td> <td>0.16667 </td> <td align="left"><span style="display:none;">0.16667</span><div style="width:33.334px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>3 / 12</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 30° - cos 60°) / 2</td> <td>0.18301 </td> <td align="left"><span style="display:none;">0.18301</span><div style="width:36.602px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 60°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">3 </th> <td>Rule</td> <td>3 / 12</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>6 / 12</td> <td>0.5 </td> <td align="left"><span style="display:none;">0.5</span><div style="width:100px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 60° - cos 90°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 90°) / 2</td> <td>0.5 </td> <td align="left"><span style="display:none;">0.5</span><div style="width:100px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">4 </th> <td>Rule</td> <td>3 / 12</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>9 / 12</td> <td>0.75 </td> <td align="left"><span style="display:none;">0.75</span><div style="width:150px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 90° - cos 120°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 120°) / 2</td> <td>0.75 </td> <td align="left"><span style="display:none;">0.75</span><div style="width:150px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">5 </th> <td>Rule</td> <td>2 / 12</td> <td>0.16667 </td> <td align="left"><span style="display:none;">0.16667</span><div style="width:33.334px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>11 / 12</td> <td>0.91667 </td> <td align="left"><span style="display:none;">0.91667</span><div style="width:183.334px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 120° - cos 150°) / 2</td> <td>0.18301 </td> <td align="left"><span style="display:none;">0.18301</span><div style="width:36.602px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 150°) / 2</td> <td>0.93301 </td> <td align="left"><span style="display:none;">0.93301</span><div style="width:186.602px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">6 </th> <td>Rule</td> <td>1 / 12</td> <td>0.08333 </td> <td align="left"><span style="display:none;">0.08333</span><div style="width:16.666px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>12 / 12</td> <td>1 </td> <td align="left"><span style="display:none;">1</span><div style="width:200px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 150° - cos 180°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 180°) / 2</td> <td>1 </td> <td align="left"><span style="display:none;">1</span><div style="width:200px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=2" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Rule_of_twelfths_circle_approximation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Rule_of_twelfths_circle_approximation.svg/220px-Rule_of_twelfths_circle_approximation.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Rule_of_twelfths_circle_approximation.svg/330px-Rule_of_twelfths_circle_approximation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Rule_of_twelfths_circle_approximation.svg/440px-Rule_of_twelfths_circle_approximation.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>A regular dodecahedron (grey) approximated with a lattice polygon using the rule of twelfths (red)</figcaption></figure> <p>In many parts of the world the tides approximate to a semi-diurnal sine curve, that is there are two high- and two low- tides per day. As an estimate then each period equates to 1 hour, with the tide rising by 1, 2, 3, 3, 2, finally 1 twelfths of its total range in each hour, from low tide to high tide in about 6 hours, then the tide is decreasing by the same pattern in the next 6 hours, back to low tide. In places where there is only one high and one low water per day, the rule can be used by assuming the steps are 2 hours. If the tidal curve does not approximate to a sine wave then the rule cannot be used.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> This is important when navigating a <a href="/wiki/Boat" title="Boat">boat</a> or a <a href="/wiki/Ship" title="Ship">ship</a> in shallow water, and when launching and retrieving boats on <a href="/wiki/Slipway" title="Slipway">slipways</a> on a tidal shore.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The rule is also useful for estimating the monthly change in sunrise and sunset and thus day length.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Example_calculations">Example calculations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=3" title="Edit section: Example calculations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Tides">Tides</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=4" title="Edit section: Tides"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If a <a href="/wiki/Tide_table" title="Tide table">tide table</a> gives the information that tomorrow's low water would be at noon and that the water level at this time would be two metres above <a href="/wiki/Chart_datum" title="Chart datum">chart datum</a>, and that at the following high tide the water level would be 14 metres, then the height of water at 3:00 p.m. can be calculated as follows: </p> <ul><li>The total increase in water level between low and high tide would be: 14 - 2 = 12 metres.</li> <li>In the first hour the water level would rise by 1 twelfth of the total (12 m) or: 1 m</li> <li>In the second hour the water level would rise by another 2 twelfths of the total (12 m) or: 2 m</li> <li>In the third hour the water level would rise by another 3 twelfths of the total (12 m) or: 3 m</li> <li>This gives the increase in the water level by 3:00 p.m. as <b>6 metres</b>.</li></ul> <p>This represents only the increase - the total depth of the water (relative to chart datum) will include the 2 m depth at low tide: 6 m + 2 m = 8 metres. </p><p>The calculation can be simplified by adding twelfths together and reducing the fraction beforehand: </p> <dl><dd>Rise of tide in three hours <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =\left({1 \over 12}+{2 \over 12}+{3 \over 12}\right)\times 12\ \mathrm {m} =\left({6 \over 12}\right)\times 12\ \mathrm {m} =\left({1 \over 2}\right)\times 12\ \mathrm {m} =6\ \mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>12</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>12</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>12</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>12</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <mn>12</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>12</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>12</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> <mo>=</mo> <mn>6</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =\left({1 \over 12}+{2 \over 12}+{3 \over 12}\right)\times 12\ \mathrm {m} =\left({6 \over 12}\right)\times 12\ \mathrm {m} =\left({1 \over 2}\right)\times 12\ \mathrm {m} =6\ \mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bd0c16880bb278465387ef232872f73139f25fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:69.06ex; height:6.176ex;" alt="{\displaystyle =\left({1 \over 12}+{2 \over 12}+{3 \over 12}\right)\times 12\ \mathrm {m} =\left({6 \over 12}\right)\times 12\ \mathrm {m} =\left({1 \over 2}\right)\times 12\ \mathrm {m} =6\ \mathrm {m} }"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Daylength">Daylength</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=5" title="Edit section: Daylength"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If midwinter sunrise and set are at 09:00 and 15:00, and midsummer at 03:00 and 21:00, the <a href="/wiki/Daytime" title="Daytime">daylight duration</a> will shift by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 over the six months from one solstice to the other. Likewise the day length changes by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 each month. More equatorial latitudes change by less, but still in the same proportions; more polar by more. </p> <div class="mw-heading mw-heading2"><h2 id="Caveats">Caveats</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=6" title="Edit section: Caveats"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rule is a rough approximation only and should be applied with great caution when used for navigational purposes. Officially produced tide tables should be used in preference whenever possible. </p><p>The rule assumes that all tides behave in a regular manner, this is not true of some geographical locations, such as <a href="/wiki/Poole_Harbour" title="Poole Harbour">Poole Harbour</a><sup id="cite_ref-Heritage_5-0" class="reference"><a href="#cite_note-Heritage-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> or the <a href="/wiki/Solent" class="mw-redirect" title="Solent">Solent</a><sup id="cite_ref-Ridge_6-0" class="reference"><a href="#cite_note-Ridge-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> where there are "double" high waters or <a href="/wiki/Weymouth_Bay" title="Weymouth Bay">Weymouth Bay</a><sup id="cite_ref-Heritage_5-1" class="reference"><a href="#cite_note-Heritage-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> where there is a double low water. </p><p>The rule assumes that the period between high and low tides is six hours but this is an underestimate and can vary anyway. </p> <div class="mw-heading mw-heading2"><h2 id="Refinement">Refinement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=7" title="Edit section: Refinement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The rule relies on the approximation of tan 60° or √3 (~1.732) with 5/3 (~1.667) yielding 3.77% error. The next best <a href="/wiki/Continued_fraction#Examples_of_rational_and_irrational_numbers" title="Continued fraction">rational approximation</a>, 7/4 (1.75) yields 1.04% error. The steps are 1:3:4:4:3:1 giving a total change of 16/16:<sup id="cite_ref-bizony_7-0" class="reference"><a href="#cite_note-bizony-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th rowspan="2">Period</th> <th rowspan="2">Rule or<br />actual<br />values </th> <th colspan="3">Increment</th> <th colspan="3">Cumulative </th></tr> <tr> <th>Exact value</th> <th>Decimal</th> <th>Relative size</th> <th>Exact value</th> <th>Decimal</th> <th>Relative size </th></tr> <tr> <th rowspan="2">1 </th> <td>Rule</td> <td>1 / 16</td> <td>0.0625 </td> <td align="left"><span style="display:none;">0.0625</span><div style="width:12.5px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>1 / 16</td> <td>0.0625 </td> <td align="left"><span style="display:none;">0.0625</span><div style="width:12.5px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 0° - cos 30°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 30°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">2 </th> <td>Rule</td> <td>3 / 16</td> <td>0.1875 </td> <td align="left"><span style="display:none;">0.1875</span><div style="width:37.5px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>4 / 16</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 30° - cos 60°) / 2</td> <td>0.18301 </td> <td align="left"><span style="display:none;">0.18301</span><div style="width:36.602px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 60°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">3 </th> <td>Rule</td> <td>4 / 16</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>8 / 16</td> <td>0.5 </td> <td align="left"><span style="display:none;">0.5</span><div style="width:100px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 60° - cos 90°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 90°) / 2</td> <td>0.5 </td> <td align="left"><span style="display:none;">0.5</span><div style="width:100px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">4 </th> <td>Rule</td> <td>4 / 16</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>12 / 16</td> <td>0.75 </td> <td align="left"><span style="display:none;">0.75</span><div style="width:150px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 90° - cos 120°) / 2</td> <td>0.25 </td> <td align="left"><span style="display:none;">0.25</span><div style="width:50px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 120°) / 2</td> <td>0.75 </td> <td align="left"><span style="display:none;">0.75</span><div style="width:150px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">5 </th> <td>Rule</td> <td>3 / 16</td> <td>0.1875 </td> <td align="left"><span style="display:none;">0.1875</span><div style="width:37.5px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>15 / 16</td> <td>0.9375 </td> <td align="left"><span style="display:none;">0.9375</span><div style="width:187.5px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 120° - cos 150°) / 2</td> <td>0.18301 </td> <td align="left"><span style="display:none;">0.18301</span><div style="width:36.602px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 150°) / 2</td> <td>0.93301 </td> <td align="left"><span style="display:none;">0.93301</span><div style="width:186.602px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <th rowspan="2">6 </th> <td>Rule</td> <td>1 / 16</td> <td>0.0625 </td> <td align="left"><span style="display:none;">0.0625</span><div style="width:12.5px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>16 / 16</td> <td>1 </td> <td align="left"><span style="display:none;">1</span><div style="width:200px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr> <tr> <td>Actual</td> <td>(cos 150° - cos 180°) / 2</td> <td>0.06699 </td> <td align="left"><span style="display:none;">0.06699</span><div style="width:13.398px;height:2ex;background:#aaa;color:inherit;"> </div></td> <td>(1 - cos 180°) / 2</td> <td>1 </td> <td align="left"><span style="display:none;">1</span><div style="width:200px;height:2ex;background:#aaa;color:inherit;"> </div> </td></tr></tbody></table> <p>The following best approximations are 19/11 (0.276% error) with steps 3:8:11:11:8:3, and 26/15 (0.074% error) with steps 4:11:15:15:11:4.<sup id="cite_ref-bizony_7-1" class="reference"><a href="#cite_note-bizony-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rule_of_twelfths&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.diy-wood-boat.com/Rule_of_twelfths.html">"Rule of Twelfths for quick tidal estimates"</a>. <i>DIY Wood Boat</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 December</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=DIY+Wood+Boat&rft.atitle=Rule+of+Twelfths+for+quick+tidal+estimates&rft_id=http%3A%2F%2Fwww.diy-wood-boat.com%2FRule_of_twelfths.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGetchell1994" class="citation book cs1">Getchell, David R. (1994). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/outboardboatersh00getc"><i>The Outboard Boater's Handbook: Advanced Seamanship and Practical Skills</i></a></span>. International Marine. p. <a rel="nofollow" class="external text" href="https://archive.org/details/outboardboatersh00getc/page/195">195</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-023053-8" title="Special:BookSources/978-0-07-023053-8"><bdi>978-0-07-023053-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Outboard+Boater%27s+Handbook%3A+Advanced+Seamanship+and+Practical+Skills&rft.pages=195&rft.pub=International+Marine&rft.date=1994&rft.isbn=978-0-07-023053-8&rft.aulast=Getchell&rft.aufirst=David+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foutboardboatersh00getc&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSweet2004" class="citation book cs1">Sweet, Robert J. (16 September 2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/weekendnavigator0000swee/page/162"><i>The Weekend Navigator: Simple Boat Navigation with GPS and Electronics</i></a></span>. McGraw Hill Professional. p. <a rel="nofollow" class="external text" href="https://archive.org/details/weekendnavigator0000swee/page/162">162</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-143035-7" title="Special:BookSources/978-0-07-143035-7"><bdi>978-0-07-143035-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Weekend+Navigator%3A+Simple+Boat+Navigation+with+GPS+and+Electronics&rft.pages=162&rft.pub=McGraw+Hill+Professional&rft.date=2004-09-16&rft.isbn=978-0-07-143035-7&rft.aulast=Sweet&rft.aufirst=Robert+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fweekendnavigator0000swee%2Fpage%2F162&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcAdam2019" class="citation web cs1">McAdam, Marcus (14 November 2019). <a rel="nofollow" class="external text" href="https://www.mc2photography.com/the-rule-of-twelfths/">"The Rule of Twelfths"</a>. <i>Mc2Photography.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-11</span></span>. <q>The same Rule of Twelfths can be applied to the duration of the days.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mc2Photography.com&rft.atitle=The+Rule+of+Twelfths&rft.date=2019-11-14&rft.aulast=McAdam&rft.aufirst=Marcus&rft_id=https%3A%2F%2Fwww.mc2photography.com%2Fthe-rule-of-twelfths%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> <li id="cite_note-Heritage-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Heritage_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Heritage_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeritage" class="citation web cs1">Heritage, Trevor. <a rel="nofollow" class="external text" href="http://www.shrimperowners.org/sitefiles/Poole%20Tides.pdf">"Poole Harbour and its tides"</a> <span class="cs1-format">(PDF)</span>. <i>Shrimperowners</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 December</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Shrimperowners&rft.atitle=Poole+Harbour+and+its+tides&rft.aulast=Heritage&rft.aufirst=Trevor&rft_id=http%3A%2F%2Fwww.shrimperowners.org%2Fsitefiles%2FPoole%2520Tides.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> <li id="cite_note-Ridge-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ridge_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRidge" class="citation web cs1">Ridge, M J, FRICS MCIT. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090822144340/http://www.bristolnomads.org.uk/stuff/double_tides.htm">"English Channel double tides"</a>. <i>Bristol Nomads windsurfing club</i>. Archived from <a rel="nofollow" class="external text" href="http://www.bristolnomads.org.uk/stuff/double_tides.htm">the original</a> on 22 August 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">19 December</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bristol+Nomads+windsurfing+club&rft.atitle=English+Channel+double+tides&rft.aulast=Ridge&rft.aufirst=M+J%2C+FRICS+MCIT&rft_id=http%3A%2F%2Fwww.bristolnomads.org.uk%2Fstuff%2Fdouble_tides.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-bizony-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-bizony_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bizony_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBizony2014" class="citation journal cs1">Bizony, Marcus Bizony (1 June 2014). <a rel="nofollow" class="external text" href="http://journals.co.za/doi/epdf/10.10520/EJC157637">"Finding rational approximations to square roots"</a>. <i>Learning and Teaching Mathematics</i>. <b>2014</b> (16)<span class="reference-accessdate">. Retrieved <span class="nowrap">25 March</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Learning+and+Teaching+Mathematics&rft.atitle=Finding+rational+approximations+to+square+roots&rft.volume=2014&rft.issue=16&rft.date=2014-06-01&rft.aulast=Bizony&rft.aufirst=Marcus+Bizony&rft_id=http%3A%2F%2Fjournals.co.za%2Fdoi%2Fepdf%2F10.10520%2FEJC157637&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARule+of+twelfths" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output 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class="navbox-group" style="width:1%"><a href="/wiki/Ocean_current" title="Ocean current">Circulation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Atmospheric_circulation" title="Atmospheric circulation">Atmospheric circulation</a></li> <li><a href="/wiki/Baroclinity" title="Baroclinity">Baroclinity</a></li> <li><a href="/wiki/Boundary_current" title="Boundary current">Boundary current</a></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis force</a></li> <li><a href="/wiki/Coriolis%E2%80%93Stokes_force" title="Coriolis–Stokes force">Coriolis–Stokes force</a></li> <li><a href="/wiki/Craik%E2%80%93Leibovich_vortex_force" title="Craik–Leibovich vortex force">Craik–Leibovich vortex force</a></li> <li><a href="/wiki/Downwelling" title="Downwelling">Downwelling</a></li> <li><a href="/wiki/Eddy_(fluid_dynamics)" title="Eddy (fluid dynamics)">Eddy</a></li> <li><a href="/wiki/Ekman_layer" title="Ekman layer">Ekman layer</a></li> <li><a href="/wiki/Ekman_spiral" title="Ekman spiral">Ekman spiral</a></li> <li><a href="/wiki/Ekman_transport" title="Ekman transport">Ekman transport</a></li> <li><a href="/wiki/El_Ni%C3%B1o%E2%80%93Southern_Oscillation" title="El Niño–Southern Oscillation">El Niño–Southern Oscillation</a></li> <li><a href="/wiki/General_circulation_model" title="General circulation model">General circulation model</a></li> <li><a href="/wiki/Geochemical_Ocean_Sections_Study" title="Geochemical Ocean Sections Study">Geochemical Ocean Sections Study</a></li> <li><a href="/wiki/Geostrophic_current" title="Geostrophic current">Geostrophic current</a></li> <li><a href="/wiki/Global_Ocean_Data_Analysis_Project" title="Global Ocean Data Analysis Project">Global Ocean Data Analysis Project</a></li> <li><a href="/wiki/Gulf_Stream" title="Gulf Stream">Gulf Stream</a></li> <li><a href="/wiki/Humboldt_Current" title="Humboldt Current">Humboldt Current</a></li> <li><a href="/wiki/Hydrothermal_circulation" title="Hydrothermal circulation">Hydrothermal circulation</a></li> <li><a href="/wiki/Langmuir_circulation" title="Langmuir circulation">Langmuir circulation</a></li> <li><a href="/wiki/Longshore_drift" title="Longshore drift">Longshore drift</a></li> <li><a href="/wiki/Loop_Current" title="Loop Current">Loop Current</a></li> <li><a href="/wiki/Modular_Ocean_Model" title="Modular Ocean Model">Modular Ocean Model</a></li> <li><a href="/wiki/Ocean_current" title="Ocean current">Ocean current</a></li> <li><a href="/wiki/Ocean_dynamical_thermostat" title="Ocean dynamical thermostat">Ocean dynamical thermostat</a></li> <li><a href="/wiki/Ocean_dynamics" title="Ocean dynamics">Ocean dynamics</a></li> <li><a href="/wiki/Ocean_gyre" title="Ocean gyre">Ocean gyre</a></li> <li><a href="/wiki/Overflow_(oceanography)" title="Overflow (oceanography)">Overflow</a></li> <li><a href="/wiki/Princeton_Ocean_Model" title="Princeton Ocean Model">Princeton Ocean Model</a></li> <li><a href="/wiki/Rip_current" title="Rip current">Rip current</a></li> <li><a href="/wiki/Subsurface_ocean_current" title="Subsurface ocean current">Subsurface ocean current</a></li> <li><a href="/wiki/Sverdrup_balance" title="Sverdrup balance">Sverdrup balance</a></li> <li><a href="/wiki/Thermohaline_circulation" title="Thermohaline circulation">Thermohaline circulation</a> <ul><li><a href="/wiki/Shutdown_of_thermohaline_circulation" class="mw-redirect" title="Shutdown of thermohaline circulation">shutdown</a></li></ul></li> <li><a href="/wiki/Upwelling" title="Upwelling">Upwelling</a></li> <li><a href="/wiki/Whirlpool" title="Whirlpool">Whirlpool</a></li> <li><a href="/wiki/Wind_generated_current" title="Wind generated current">Wind generated current</a></li> <li><a href="/wiki/World_Ocean_Circulation_Experiment" title="World Ocean Circulation Experiment">World Ocean Circulation Experiment</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Tide" title="Tide">Tides</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amphidromic_point" title="Amphidromic point">Amphidromic point</a></li> <li><a href="/wiki/Earth_tide" title="Earth tide">Earth tide</a></li> <li><a href="/wiki/Head_of_tide" title="Head of tide">Head of tide</a></li> <li><a href="/wiki/Internal_tide" title="Internal tide">Internal tide</a></li> <li><a href="/wiki/Lunitidal_interval" title="Lunitidal interval">Lunitidal interval</a></li> <li><a href="/wiki/Perigean_spring_tide" title="Perigean spring tide">Perigean spring tide</a></li> <li><a href="/wiki/Rip_tide" title="Rip tide">Rip tide</a></li> <li><a class="mw-selflink selflink">Rule of twelfths</a></li> <li><a href="/wiki/Slack_tide" title="Slack tide">Slack tide</a></li> <li><a href="/wiki/Theory_of_tides" title="Theory of tides">Theory of tides</a></li> <li><a href="/wiki/Tidal_bore" title="Tidal bore">Tidal bore</a></li> <li><a href="/wiki/Tidal_force" title="Tidal force">Tidal force</a></li> <li><a href="/wiki/Tidal_power" title="Tidal power">Tidal power</a></li> <li><a href="/wiki/Tidal_race" title="Tidal race">Tidal race</a></li> <li><a href="/wiki/Tidal_range" title="Tidal range">Tidal range</a></li> <li><a href="/wiki/Tidal_resonance" title="Tidal resonance">Tidal resonance</a></li> <li><a href="/wiki/Tide_gauge" title="Tide gauge">Tide gauge</a></li> <li><a href="/wiki/Tideline" title="Tideline">Tideline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Landform" title="Landform">Landforms</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abyssal_fan" title="Abyssal fan">Abyssal fan</a></li> <li><a href="/wiki/Abyssal_plain" title="Abyssal plain">Abyssal plain</a></li> <li><a href="/wiki/Atoll" title="Atoll">Atoll</a></li> <li><a href="/wiki/Bathymetric_chart" title="Bathymetric chart">Bathymetric chart</a></li> <li><a href="/wiki/Carbonate_platform" title="Carbonate platform">Carbonate platform</a></li> <li><a href="/wiki/Coastal_geography" title="Coastal geography">Coastal geography</a></li> <li><a href="/wiki/Cold_seep" title="Cold seep">Cold seep</a></li> <li><a href="/wiki/Continental_margin" title="Continental margin">Continental margin</a></li> <li><a href="/wiki/Continental_rise" title="Continental rise">Continental rise</a></li> <li><a href="/wiki/Continental_shelf" title="Continental shelf">Continental shelf</a></li> <li><a href="/wiki/Contourite" title="Contourite">Contourite</a></li> <li><a href="/wiki/Guyot" title="Guyot">Guyot</a></li> <li><a href="/wiki/Hydrography" title="Hydrography">Hydrography</a></li> <li><a href="/wiki/Knoll_(oceanography)" title="Knoll (oceanography)">Knoll</a></li> <li><a href="/wiki/Ocean_bank" title="Ocean bank">Ocean bank</a></li> <li><a href="/wiki/Oceanic_basin" title="Oceanic basin">Oceanic basin</a></li> <li><a href="/wiki/Oceanic_plateau" title="Oceanic plateau">Oceanic plateau</a></li> <li><a href="/wiki/Oceanic_trench" title="Oceanic trench">Oceanic trench</a></li> <li><a href="/wiki/Passive_margin" title="Passive margin">Passive margin</a></li> <li><a href="/wiki/Seabed" title="Seabed">Seabed</a></li> <li><a href="/wiki/Seamount" title="Seamount">Seamount</a></li> <li><a href="/wiki/Submarine_canyon" title="Submarine canyon">Submarine canyon</a></li> <li><a href="/wiki/Submarine_volcano" title="Submarine volcano">Submarine volcano</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Plate_tectonics" title="Plate tectonics">Plate<br />tectonics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Convergent_boundary" title="Convergent boundary">Convergent boundary</a></li> <li><a href="/wiki/Divergent_boundary" title="Divergent boundary">Divergent boundary</a></li> <li><a href="/wiki/Fracture_zone" title="Fracture zone">Fracture zone</a></li> <li><a href="/wiki/Hydrothermal_vent" title="Hydrothermal vent">Hydrothermal vent</a></li> <li><a href="/wiki/Marine_geology" title="Marine geology">Marine geology</a></li> <li><a href="/wiki/Mid-ocean_ridge" title="Mid-ocean ridge">Mid-ocean ridge</a></li> <li><a href="/wiki/Mohorovi%C4%8Di%C4%87_discontinuity" title="Mohorovičić discontinuity">Mohorovičić discontinuity</a></li> <li><a href="/wiki/Oceanic_crust" title="Oceanic crust">Oceanic crust</a></li> <li><a href="/wiki/Outer_trench_swell" title="Outer trench swell">Outer trench swell</a></li> <li><a href="/wiki/Ridge_push" title="Ridge push">Ridge push</a></li> <li><a href="/wiki/Seafloor_spreading" title="Seafloor spreading">Seafloor spreading</a></li> <li><a href="/wiki/Slab_pull" title="Slab pull">Slab pull</a></li> <li><a href="/wiki/Slab_suction" title="Slab suction">Slab suction</a></li> <li><a href="/wiki/Slab_window" title="Slab window">Slab window</a></li> <li><a href="/wiki/Subduction" title="Subduction">Subduction</a></li> <li><a href="/wiki/Transform_fault" title="Transform fault">Transform fault</a></li> <li><a href="/wiki/Vine%E2%80%93Matthews%E2%80%93Morley_hypothesis" title="Vine–Matthews–Morley hypothesis">Vine–Matthews–Morley hypothesis</a></li> <li><a href="/wiki/Volcanic_arc" title="Volcanic arc">Volcanic arc</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ocean zones</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Benthic_zone" title="Benthic zone">Benthic</a></li> <li><a href="/wiki/Deep_ocean_water" title="Deep ocean water">Deep ocean water</a></li> <li><a href="/wiki/Deep_sea" title="Deep sea">Deep sea</a></li> <li><a href="/wiki/Littoral_zone" title="Littoral zone">Littoral</a></li> <li><a href="/wiki/Mesopelagic_zone" title="Mesopelagic zone">Mesopelagic</a></li> <li><a href="/wiki/Oceanic_zone" title="Oceanic zone">Oceanic</a></li> <li><a href="/wiki/Pelagic_zone" title="Pelagic zone">Pelagic</a></li> <li><a href="/wiki/Photic_zone" title="Photic zone">Photic</a></li> <li><a href="/wiki/Surf_zone" title="Surf zone">Surf</a></li> <li><a href="/wiki/Swash" title="Swash">Swash</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Sea_level" title="Sea level">Sea level</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Deep-ocean_Assessment_and_Reporting_of_Tsunamis" title="Deep-ocean Assessment and Reporting of Tsunamis">Deep-ocean Assessment and Reporting of Tsunamis</a></li> <li><a href="/wiki/Global_Sea_Level_Observing_System" title="Global Sea Level Observing System">Global Sea Level Observing System</a></li> <li><a href="/wiki/North_West_Shelf_Operational_Oceanographic_System" title="North West Shelf Operational Oceanographic System">North West Shelf Operational Oceanographic System</a></li> <li><a href="/wiki/Sea-level_curve" title="Sea-level curve">Sea-level curve</a></li> <li><a href="/wiki/Sea_level_drop" title="Sea level drop">Sea level drop</a></li> <li><a href="/wiki/Sea_level_rise" title="Sea level rise">Sea level rise</a></li> <li><a href="/wiki/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Acoustical_oceanography" class="mw-redirect" title="Acoustical oceanography">Acoustics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Deep_scattering_layer" title="Deep scattering layer">Deep scattering layer</a></li> <li><a href="/wiki/Ocean_acoustic_tomography" title="Ocean acoustic tomography">Ocean acoustic tomography</a></li> <li><a href="/wiki/Sofar_bomb" title="Sofar bomb">Sofar bomb</a></li> <li><a href="/wiki/SOFAR_channel" title="SOFAR channel">SOFAR channel</a></li> <li><a href="/wiki/Underwater_acoustics" title="Underwater acoustics">Underwater acoustics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Satellites</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jason-1" title="Jason-1">Jason-1</a></li> <li><a href="/wiki/OSTM/Jason-2" title="OSTM/Jason-2">OSTM/Jason-2</a></li> <li><a href="/wiki/Jason-3" title="Jason-3">Jason-3</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ocean_acidification" title="Ocean acidification">Acidification</a></li> <li><a href="/wiki/Argo_(oceanography)" title="Argo (oceanography)">Argo</a></li> <li><a href="/wiki/Benthic_lander" title="Benthic lander">Benthic lander</a></li> <li><a href="/wiki/Color_of_water" title="Color of water">Color of water</a></li> <li><a href="/wiki/DSV_Alvin" title="DSV Alvin">DSV <i>Alvin</i></a></li> <li><a href="/wiki/Marginal_sea" class="mw-redirect" title="Marginal sea">Marginal sea</a></li> <li><a href="/wiki/Marine_energy" title="Marine energy">Marine energy</a></li> <li><a href="/wiki/Marine_pollution" title="Marine pollution">Marine pollution</a></li> <li><a href="/wiki/Mooring_(oceanography)" title="Mooring (oceanography)">Mooring</a></li> <li><a href="/wiki/National_Oceanographic_Data_Center" title="National Oceanographic Data Center">National Oceanographic Data Center</a></li> <li><a href="/wiki/Ocean" title="Ocean">Ocean</a></li> <li><a href="/wiki/Ocean_exploration" title="Ocean exploration">Explorations</a></li> <li><a href="/wiki/Ocean_observations" title="Ocean observations">Observations</a></li> <li><a href="/wiki/Ocean_reanalysis" title="Ocean reanalysis">Reanalysis</a></li> <li><a href="/wiki/Ocean_surface_topography" title="Ocean surface topography">Ocean surface topography</a></li> <li><a href="/wiki/Ocean_temperature" title="Ocean temperature">Ocean temperature</a></li> <li><a href="/wiki/Ocean_thermal_energy_conversion" title="Ocean thermal energy conversion">Ocean thermal energy conversion</a></li> <li><a href="/wiki/Oceanography" title="Oceanography">Oceanography</a> <ul><li><a href="/wiki/Outline_of_oceanography" title="Outline of oceanography">Outline of oceanography</a></li></ul></li> <li><a href="/wiki/Pelagic_sediment" title="Pelagic sediment">Pelagic sediment</a></li> <li><a href="/wiki/Sea_surface_microlayer" title="Sea surface microlayer">Sea surface microlayer</a></li> <li><a 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