1621 lines
31 KiB
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1621 lines
31 KiB
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.constants"></a><a class="link" href="constants.html" title="The Mathematical Constants">The Mathematical Constants</a>
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</h2></div></div></div>
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<p>
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This section lists the mathematical constants, their use(s) (and sometimes
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rationale for their inclusion).
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</p>
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<div class="table">
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<a name="math_toolkit.constants.mathematical_constants"></a><p class="title"><b>Table 4.1. Mathematical Constants</b></p>
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<div class="table-contents"><table class="table" summary="Mathematical Constants">
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<colgroup>
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<col>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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name
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</p>
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</th>
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<th>
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<p>
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formula
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</p>
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</th>
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<th>
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<p>
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Value (6 decimals)
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</p>
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</th>
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<th>
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<p>
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Uses and Rationale
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>Rational fractions</strong></span>
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</p>
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</td>
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<td>
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</td>
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<td>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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half
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</p>
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</td>
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<td>
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<p>
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1/2
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</p>
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</td>
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<td>
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<p>
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0.5
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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third
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</p>
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</td>
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<td>
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<p>
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1/3
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</p>
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</td>
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<td>
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<p>
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0.333333
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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two_thirds
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</p>
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</td>
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<td>
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<p>
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2/3
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</p>
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</td>
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<td>
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<p>
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0.66667
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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three_quarters
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</p>
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</td>
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<td>
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<p>
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3/4
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</p>
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</td>
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<td>
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<p>
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0.75
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<span class="bold"><strong>two and related</strong></span>
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</p>
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</td>
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<td>
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</td>
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<td>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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root_two
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</p>
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</td>
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<td>
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<p>
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√2
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</p>
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</td>
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<td>
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<p>
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1.41421
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</p>
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</td>
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<td>
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<p>
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Equivalent to POSIX constant M_SQRT2
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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root_three
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</p>
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</td>
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<td>
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<p>
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√3
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</p>
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</td>
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<td>
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<p>
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1.73205
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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half_root_two
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</p>
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</td>
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<td>
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<p>
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√2 /2
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</p>
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</td>
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<td>
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<p>
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0.707106
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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ln_two
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</p>
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</td>
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<td>
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<p>
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ln(2)
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</p>
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</td>
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<td>
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<p>
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0.693147
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</p>
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</td>
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<td>
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<p>
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Equivalent to POSIX constant M_LN2
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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ln_ten
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</p>
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</td>
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<td>
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<p>
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ln(10)
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</p>
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</td>
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<td>
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<p>
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2.30258
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</p>
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</td>
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<td>
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<p>
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Equivalent to POSIX constant M_LN10
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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ln_ln_two
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</p>
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</td>
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<td>
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<p>
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ln(ln(2))
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</p>
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</td>
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<td>
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<p>
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-0.366512
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</p>
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</td>
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<td>
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<p>
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Gumbel distribution median
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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root_ln_four
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</p>
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</td>
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<td>
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<p>
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√ln(4)
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</p>
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</td>
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<td>
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<p>
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1.177410
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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one_div_root_two
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</p>
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</td>
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<td>
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<p>
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1/√2
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</p>
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</td>
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<td>
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<p>
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0.707106
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</p>
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</td>
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<td>
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<p>
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Equivalent to POSIX constant M_SQRT1_2
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</p>
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</td>
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</tr>
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<tr>
|
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<td>
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<p>
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<span class="bold"><strong>π and related</strong></span>
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</p>
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</td>
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<td>
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</td>
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<td>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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|
pi
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</p>
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</td>
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<td>
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<p>
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pi
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</p>
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</td>
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<td>
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<p>
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3.14159
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</p>
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</td>
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<td>
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<p>
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|
Ubiquitous. Archimedes constant <a href="http://en.wikipedia.org/wiki/Pi" target="_top">π</a>.
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Equivalent to POSIX constant M_PI
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</p>
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</td>
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</tr>
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<tr>
|
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<td>
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<p>
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half_pi
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</p>
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</td>
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<td>
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<p>
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π/2
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</p>
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</td>
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<td>
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<p>
|
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1.570796
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</p>
|
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</td>
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<td>
|
|
<p>
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Equivalent to POSIX constant M_PI2
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</p>
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</td>
|
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</tr>
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<tr>
|
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<td>
|
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<p>
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|
third_pi
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</p>
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</td>
|
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<td>
|
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<p>
|
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π/3
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</p>
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</td>
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<td>
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<p>
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1.04719
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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quarter_pi
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</p>
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</td>
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<td>
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<p>
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π/4
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</p>
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</td>
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<td>
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<p>
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0.78539816
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</p>
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</td>
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<td>
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<p>
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Equivalent to POSIX constant M_PI_4
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</p>
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</td>
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</tr>
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<tr>
|
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<td>
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<p>
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sixth_pi
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</p>
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</td>
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<td>
|
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<p>
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π/6
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</p>
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</td>
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<td>
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<p>
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0.523598
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</p>
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</td>
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<td>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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two_pi
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</p>
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</td>
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<td>
|
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<p>
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2π
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</p>
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</td>
|
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<td>
|
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<p>
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6.28318
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</p>
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</td>
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<td>
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<p>
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Many uses, most simply, circumference of a circle
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</p>
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</td>
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</tr>
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<tr>
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<td>
|
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<p>
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two_thirds_pi
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</p>
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</td>
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<td>
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<p>
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2/3 π
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</p>
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</td>
|
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<td>
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<p>
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2.09439
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</p>
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</td>
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<td>
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<p>
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<a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
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of a hemi-sphere</a> = 4/3 π r³
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</p>
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</td>
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</tr>
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<tr>
|
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<td>
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<p>
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three_quarters_pi
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</p>
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</td>
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<td>
|
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<p>
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3/4 π
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</p>
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</td>
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<td>
|
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<p>
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2.35619
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</p>
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</td>
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<td>
|
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<p>
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= 3/4 π
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</p>
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</td>
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</tr>
|
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<tr>
|
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<td>
|
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<p>
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|
four_thirds_pi
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</p>
|
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</td>
|
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<td>
|
|
<p>
|
|
4/3 π
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
4.18879
|
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere" target="_top">volume
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of a sphere</a> = 4/3 π r³
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</p>
|
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</td>
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</tr>
|
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<tr>
|
|
<td>
|
|
<p>
|
|
one_div_two_pi
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</p>
|
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</td>
|
|
<td>
|
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<p>
|
|
1/(2π)
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
|
1.59155
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</p>
|
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</td>
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<td>
|
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<p>
|
|
Widely used
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</p>
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</td>
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</tr>
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<tr>
|
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<td>
|
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<p>
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|
root_pi
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</p>
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</td>
|
|
<td>
|
|
<p>
|
|
√π
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</p>
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</td>
|
|
<td>
|
|
<p>
|
|
1.77245
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Widely used
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
root_half_pi
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
√ π/2
|
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.25331
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Widely used
|
|
</p>
|
|
</td>
|
|
</tr>
|
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<tr>
|
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<td>
|
|
<p>
|
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root_two_pi
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</p>
|
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</td>
|
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<td>
|
|
<p>
|
|
√ π*2
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2.50662
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Widely used
|
|
</p>
|
|
</td>
|
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</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
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one_div_pi
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</p>
|
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</td>
|
|
<td>
|
|
<p>
|
|
1/π
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</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.31830988
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Equivalent to POSIX constant M_1_PI
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
two_div_pi
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|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2/π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.63661977
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Equivalent to POSIX constant M_2_PI
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_root_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/√π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.564189
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
two_div_root_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2/√π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.128379
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Equivalent to POSIX constant M_2_SQRTPI
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_root_two_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/√(2π)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.398942
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
root_one_div_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
√(1/π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.564189
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
pi_minus_three
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
π-3
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.141593
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
four_minus_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
4 -π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.858407
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
pi_pow_e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
π<sup>e</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
22.4591
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
pi_sqr
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
π<sup>2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
9.86960
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
pi_sqr_div_six
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
π<sup>2</sup>/6
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.64493
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
pi_cubed
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
π<sup>3</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
31.00627
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
cbrt_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
√<sup>3</sup> π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.46459
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_cbrt_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/√<sup>3</sup> π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.682784
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
<span class="bold"><strong>Euler's e and related</strong></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2.71828
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/E_(mathematical_constant)" target="_top">Euler's
|
|
constant e</a>, equivalent to POSIX constant M_E
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
exp_minus_half
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
e <sup>-1/2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.606530
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
e_pow_pi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
e <sup>π</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
23.14069
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
root_e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
√ e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.64872
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
log10_e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
log10(e)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.434294
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Equivalent to POSIX constant M_LOG10E
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_log10_e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/log10(e)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2.30258
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
log2_e
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
log<sub>2</sub>(e)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.442695
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
This is the same as 1/ln(2) and is equivalent to POSIX constant M_LOG2E
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
<span class="bold"><strong>Trigonometric</strong></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
degree
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
radians = π / 180
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.017453
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
radian
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
degrees = 180 / π
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
57.2957
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sin_one
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
sin(1)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.841470
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
cos_one
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
cos(1)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.54030
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
sinh_one
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
sinh(1)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.17520
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
cosh_one
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
cosh(1)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.54308
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
<span class="bold"><strong>Phi</strong></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Phidias golden ratio
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Golden_ratio" target="_top">Phidias golden
|
|
ratio</a>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
(1 + √5) /2
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.61803
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
finance
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
ln_phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
ln(φ)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.48121
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_ln_phi
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/ln(φ)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2.07808
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
<span class="bold"><strong>Euler's Gamma</strong></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
euler
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
euler
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.577215
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" target="_top">Euler-Mascheroni
|
|
gamma constant</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
one_div_euler
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1/euler
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.73245
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
euler_sqr
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
euler<sup>2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.333177
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
<span class="bold"><strong>Misc</strong></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
<td>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
zeta_two
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
ζ(2)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.64493
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
|
|
zeta function</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
zeta_three
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
ζ(3)
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.20205
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Riemann
|
|
zeta function</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
catalan
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="emphasis"><em>K</em></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.915965
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://mathworld.wolfram.com/CatalansConstant.html" target="_top">Catalan
|
|
(or Glaisher) combinatorial constant</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
glaisher
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="emphasis"><em>A</em></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.28242
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="https://oeis.org/A074962/constant" target="_top">Decimal expansion
|
|
of Glaisher-Kinkelin constant</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
khinchin
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="emphasis"><em>k</em></span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2.685452
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="https://oeis.org/A002210/constant" target="_top">Decimal expansion
|
|
of Khinchin constant</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
extreme_value_skewness
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
12√6 ζ(3)/ π<sup>3</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
1.139547
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Extreme value distribution
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
rayleigh_skewness
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
2√π(π-3)/(4 - π)<sup>3/2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.631110
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Rayleigh distribution skewness
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
rayleigh_kurtosis_excess
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
-(6π<sup>2</sup>-24π+16)/(4-π)<sup>2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
0.245089
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">Rayleigh
|
|
distribution kurtosis excess</a>
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<td>
|
|
<p>
|
|
rayleigh_kurtosis
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
3+(6π<sup>2</sup>-24π+16)/(4-π)<sup>2</sup>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
3.245089
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
Rayleigh distribution kurtosis
|
|
</p>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><div class="note"><table border="0" summary="Note">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
|
|
<th align="left">Note</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>
|
|
Integer values are <span class="bold"><strong>not included</strong></span> in this
|
|
list of math constants, however interesting, because they can be so easily
|
|
and exactly constructed, even for UDT, for example: <code class="computeroutput"><span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_float</span><span class="special">>(</span><span class="number">42</span><span class="special">)</span></code>.
|
|
</p></td></tr>
|
|
</table></div>
|
|
<div class="tip"><table border="0" summary="Tip">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
|
|
<th align="left">Tip</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>
|
|
If you know the approximate value of the constant, you can search for the
|
|
value to find Boost.Math chosen name in this table.
|
|
</p></td></tr>
|
|
</table></div>
|
|
<div class="tip"><table border="0" summary="Tip">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
|
|
<th align="left">Tip</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>
|
|
Bernoulli numbers are available at <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
|
|
numbers</a>.
|
|
</p></td></tr>
|
|
</table></div>
|
|
<div class="tip"><table border="0" summary="Tip">
|
|
<tr>
|
|
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../doc/src/images/tip.png"></td>
|
|
<th align="left">Tip</th>
|
|
</tr>
|
|
<tr><td align="left" valign="top"><p>
|
|
Factorials are available at <a class="link" href="factorials/sf_factorial.html" title="Factorial">factorial</a>.
|
|
</p></td></tr>
|
|
</table></div>
|
|
</div>
|
|
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
|
<td align="left"></td>
|
|
<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
|
|
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
|
|
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
|
|
Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
|
|
Daryle Walker and Xiaogang Zhang<p>
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
|
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
|
</p>
|
|
</div></td>
|
|
</tr></table>
|
|
<hr>
|
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<div class="spirit-nav">
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