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    <title>MaplePrimes - comments on Post, MRB constant N part 2</title>
    <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2</link>
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    <pubDate>Wed, 10 Jun 2026 22:18:26 GMT</pubDate>
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    <description>The latest comments added to the Post, MRB constant N part 2</description>
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      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - comments on Post, MRB constant N part 2</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2</link>
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      <title>Page 2</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2?ref=Feed:MaplePrimes:MRB constant N part 2:Comments#comment99818</link>
      <itunes:summary>&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;Page 2:&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;span style="font-size: x-small;"&gt;Let x= MRB constant.&lt;/span&gt;&amp;nbsp;&amp;nbsp;Each approximation is followed by a maple input so you can verify these approximations.&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;The digits of accuracy (D.O.A.) might seem embellished by 1 digit because it is computed by the reciprocal of the magnitude of error. For instance, The Champernowne Constant = 0.1234567891011121314151617181920212223243..., and its approximation constructed from the MRB constant is (1/2)*(8647+1490*x)/(31589+24300*x).&amp;nbsp; 0.1234567891011121314151617181920212223243-(1/2)*(8647+1490*x)/(31589+24300*x)= 9.79861545008*10^(-19). Thus, according to this rule,&amp;nbsp;there&amp;nbsp;are 19 digits worth of accuracy in the approximation. However, You could argue that counting the 0, only 18 digits actually match&amp;nbsp;.&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;a href="http://mathworld.wolfram.com/FoiasConstant.html"&gt;The f&lt;/a&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/FoiasConstant.html"&gt;irst Foias constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=0c40df3719dcb8ba9a779d93060421d0.gif" alt="-(24242/16437)*Pi+35/6-(1/15)*x"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to all known digits of accuracy. &amp;nbsp;-(24242/16437)*Pi+35/6-(1/15)*x&lt;/span&gt;&lt;/span&gt; &lt;a href="http://mathworld.wolfram.com/FigureEightKnot.html"&gt;The figure eight knot hyperbolic &lt;/a&gt;volume =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=9239ab25dc44451d2044a5a7b72fc534.gif" alt="(1/4)*(-186121+6306*x)/(-22921+768*x) "&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp; to 18 digits of accuracy. (1/4)*(-186121+6306*x)/(-22921+768*x)&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/FoiasConstant.html"&gt;The second Foias constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=181967b9d490b3a7c9170ff72e3f1cb4.gif" alt=" (57063/157000)*exp(1)+777/3925+(63/7850)*x "&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to all known digits of accuracy.&amp;nbsp;&amp;nbsp; (57063/157000)*exp(1)+777/3925+(63/7850)*x&amp;nbsp;&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://oeis.org/A078416"&gt;Viswanath's constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=f0850de5bfa287f1080c8ebe0f518b4e.gif" alt="-(150/23177)*exp(1)+3800/3311+(100/9933)*x"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to all known digits of accuracy.&amp;nbsp; -(150/23177)*exp(1)+3800/3311+(100/9933)*x&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;Viswanath's constant =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=2ac90e3f5b4a752b2d757269a0382f33.gif" alt=" -1/9977"&gt;&lt;/span&gt;&lt;/span&gt;*(4704*e+23744+1792*x) to all known digits of accuracy.&amp;nbsp; -1/9977*(4704*exp(1)+23744+1792*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/SarnaksConstant.html"&gt;Sarnak constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=b759a1fbe621735f68f237d8f160c7c7.gif" alt="(1/4)*(29161-392*x)/(9960+473*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to 18 digits of accuracy.&amp;nbsp; (1/4)*(29161-392*x)/(9960+473*x)&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;Sarnak constant=&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c8e098ddc5f9a9da90c24cf9707715a9.gif" alt="(3/2)*(-159537+3418*x)/(-330691+7074*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to 18 digits of accuracy.&amp;nbsp; (3/2)*(-159537+3418*x)/(-330691+7074*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/PlasticConstant.html"&gt;Plastic Constant&lt;/a&gt;&amp;nbsp;=&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=d87aeb76cd23235ae11716cfd5e87f5b.gif" alt="(1/3)*(192917+2712*x)/(48549+650*x)"&gt;&lt;/span&gt;&lt;/span&gt; to 18 digits of accuracy.&amp;nbsp; (1/3)*(192917+2712*x)/(48549+650*x)&amp;nbsp;&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;a href="http://mathworld.wolfram.com/RutherfordConstant.html"&gt;Rutherford Constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=70b3d9524b82d6409d47ceb9de96cb2c.gif" alt="(2*(-4195+888*x))/(-10175+2036*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to 17 digits of accuracy.&amp;nbsp;&amp;nbsp; (2*(-4195+888*x))/(-10175+2036*x)&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;Rutherford Constant =&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=29cbb4eed735a37afbef14600c645878.gif" alt="(383657+33831*x)/(465607+45000*x)"&gt;&lt;/span&gt;&lt;/span&gt; to 19 digits of accuracy.&amp;nbsp; (383657+33831*x)/(465607+45000*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/TrottConstant.html"&gt;Trotts first constant&lt;/a&gt; =&amp;nbsp; &lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=32e6e33789c41ca8acb2a5add194a555.gif" alt="(6*(-492+19*x))/(-27097+344*x)"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;to 17 digits of accuracy.&amp;nbsp;&amp;nbsp; (6*(-492+19*x))/(-27097+344*x)&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;Trott's first &amp;nbsp;constant =&amp;nbsp; &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=f2c3a287adee9fbc78605157e5802204.gif" alt="(1/4)*(3167-400*x)/(7099+165*x)"&gt;&amp;nbsp;to 17 digits of accuracy. &lt;span style="font-family: Calibri; font-size: small;"&gt;(1/4)*(3167-400*x)/(7099+165*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;span style="font-family: Calibri; font-size: small;"&gt;Trott's first&amp;nbsp; constant =&amp;nbsp; &lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=4a8fdf3d9de28584fe8ab93ef8eab76e.gif" alt="(1/7)*(-2995+183*x)/(-3947+243*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 digits of accuracy.&amp;nbsp; (1/7)*(-2995+183*x)/(-3947+243*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/SierpinskiConstant.html"&gt;Sierpiński constant&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=8e03cb234cb2c9def218470ca6135d81.gif" alt="(6*(-16249+260*x))/(-118473+1822*x)"&gt;&lt;/span&gt;&lt;/span&gt; to 18 digits of accuracy.&amp;nbsp;&amp;nbsp; (6*(-16249+260*x))/(-118473+1822*x)&lt;/p&gt;
&lt;/p&gt;
&lt;p&gt;Sierpiński constant =&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=7bca7ee7d066eda61e892a6d8ab74557.gif" alt=" (-7652+81*x)/(-9550+1431*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 digits of accuracy.&amp;nbsp;&amp;nbsp;&amp;nbsp;(-7652+81*x)/(-9550+1431*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;Mean tetrahedron-in-tetrahedron volume =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=e2556ad3a400bb24d57003418d2c1f4c.gif" alt="(1/1004)*(202-279*x)/(8+3*x)"&gt;&lt;/span&gt;&lt;/span&gt; to 18 digits of accuracy.&amp;nbsp;&amp;nbsp; (1/1004)*(202-279*x)/(8+3*x)&lt;/p&gt;
&lt;p&gt;Mean tetrahedron-in-tetrahedron volume =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=e4eda78e7e79280b668583d634d0b52e.gif" alt="(2*(6377+75*x))/(739407-25150*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; to 18 digits of accuracy.&amp;nbsp; (2*(6377+75*x))/(739407-25150*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/DiskLinePicking.html"&gt;The mean line - in - disk length&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=8d58f9a7072d8e07a668a73443b6953c.gif" alt="(114341+2700*x)/(126239+3231*x)"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt; to 19 digits of accuracy. (114341+2700*x)/(126239+3231*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&lt;a href="http://oeis.org/A103983"&gt;The mean line-in-tesseract length&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=2042ae677cab058041610a4648e93dfc.gif" alt="(11/2)*(703-30*x)/(4927+27*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;to 16 digits of accuracy. (11/2)*(703-30*x)/(4927+27*x)&amp;nbsp; &lt;a href="http://mathworld.wolfram.com/PowerTower.html"&gt;The iterated exponential constant ( that is e^(-e) )&lt;/a&gt; =&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=7c171a6363e1d6c199c7e31cab9fc727.gif" alt="(1/10)*(7169+417*x)/(10856+675*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp; to 18 digits of accuracy .&amp;nbsp; (1/10)*(7169+417*x)/(10856+675*x)&amp;nbsp;&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;The iterated exponential constant =&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=37c6b6388bc5971145f6a467e1814913.gif" alt=" (5239+576*x)/(79999+5504*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy.&amp;nbsp;&amp;nbsp;&amp;nbsp;(5239+576*x)/(79999+5504*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/DiskTrianglePicking.html"&gt;The mean triangle - in - disk area (i.e. 0.0738800297...) &lt;/a&gt;=&amp;nbsp; &amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=771aaa992cdc4db052853702ec8a9298.gif" alt="(1798/79011)*Pi+188/79011+(4/79011)*x"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;to 18 digits of accuracy.&lt;/span&gt;&lt;/span&gt;&amp;nbsp; (1798/79011)*Pi+188/79011+(4/79011)*x&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;The mean triangle - in - disk area (i.e. 0.0738800297...) =&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=a3b7f20e3c42cbe902ea30189fd63539.gif" alt="(1/4)*(75679+3252*x)/(256201+10400*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; to 19 digits of accuracy.&amp;nbsp; (1/4)*(75679+3252*x)/(256201+10400*x)&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/NestedRadicalConstant.html"&gt;Nested Radical Constant&lt;/a&gt; = &amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/NestedRadicalConstant.html"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=e4e46dfa43feb10f1e445b01eb2924dd.gif" alt="(100/3)*(254+47*x)/(4790+1031*x)"&gt;&lt;/a&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy&amp;nbsp;&amp;nbsp;&amp;nbsp; (100/3)*(254+47*x)/(4790+1031*x),&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://oeis.org/A091667"&gt;Ramanujan's&amp;nbsp;first continued fraction constant&lt;/a&gt;&amp;nbsp;=&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c5cec3fc30fabc99a943eb4ac250d624.gif" alt="(1/9)*(1658+305*x)/(122+367*x)"&gt;&amp;nbsp;to 18 digits of accuracy.(1/9)*(1658+305*x)/(122+367*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/RamanujanContinuedFractions.html"&gt;Ramanujan's second continued fraction constant (i.e. 0.9999992087329&amp;hellip;)&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c8b101515d36d7d18b7d44459e6303fa.gif" alt="-(1/60)*(-25537+54*x)/(420+29*x)"&gt;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy.&amp;nbsp; -(1/60)*(-25537+54*x)/(420+29*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;
&lt;p&gt;
&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/MertensConstant.html"&gt;Mertens Constant&lt;/a&gt; =&amp;nbsp; &lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=b70300abf789333bc6984db64d8cfa28.gif" alt="(1/2)*(50959+2614*x)/(97431+5030*x)"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;to 19 digits of accuracy.&amp;nbsp; (1/2)*(50959+2614*x)/(97431+5030*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
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&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 2</description>
      <guid>99818</guid>
      <pubDate>Sat, 04 Dec 2010 01:56:24 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>Page 3:Let x= MRB constant</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2?ref=Feed:MaplePrimes:MRB constant N part 2:Comments#comment99867</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;Page 3:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: x-small;"&gt;Let x= MRB constant.&amp;nbsp;&amp;nbsp;Each approximation is followed by a maple input so you can verify these approximations.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The digits of accuracy (D.O.A.) might seem embellished by 1 digit because it is computed by the reciprocal of the magnitude of error. For instance, The Champernowne Constant = 0.1234567891011121314151617181920212223243..., and its approximation constructed from the MRB constant is (1/2)*(8647+1490*x)/(31589+24300*x).&amp;nbsp; 0.1234567891011121314151617181920212223243-(1/2)*(8647+1490*x)/(31589+24300*x)= 9.79861545008*10^(-19). Thus, according to this rule,&amp;nbsp;there&amp;nbsp;are 19 digits worth of accuracy in the approximation. However, You could argue that counting the 0, only 18 digits actually match&amp;nbsp;.&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/BrunsConstant.html"&gt;Brun's constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=3b4f24abc44e4bcad86bb1127f52a3be.gif" alt="(7273/38)*Pi-11448/19+(318/19)*x"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to at least all but the last known digit. (7273/38)*Pi-11448/19+(318/19)*x&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ContinuedFractionConstant.html"&gt;The continued fraction constant &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=2e82945a7b488a082ee2dfe44e7a2656.gif" alt="(9/2)*(99-73*x)/(541+48*x)"&gt;&amp;nbsp;&amp;nbsp;to 15 digits of accuracy.&amp;nbsp; (9/2)*(99-73*x)/(541+48*x)&lt;/p&gt;
&lt;p&gt;The Continued Fraction Constant =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=6b7d447fb99b6e47fda41a2f653de23a.gif" alt="(3826+1903*x)/(6167-913*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp; (3826+1903*x)/(6167-913*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LochsTheorem.html"&gt;Lochs' constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=5e7987050b9bd30519ff547ad1f3d2a5.gif" alt="(105/22)*(-165+8*x)/(-811+36*x)"&gt;&amp;nbsp;&amp;nbsp;to 16 digits of accuracy. (105/22)*(-165+8*x)/(-811+36*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/NortonsConstant.html"&gt;Norton's constant&lt;/a&gt; =&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c1160c64316fdcbf4b8d4596e747e79f.gif" alt=" (10*(6193+200*x))/(946338+37565*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 digits of accuracy.&amp;nbsp;&amp;nbsp;(10*(6193+200*x))/(946338+37565*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/GausssConstant.html"&gt;Gauss's Constant&lt;/a&gt;&amp;nbsp; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=17334b034f570f9b83b6f2b77414b8c4.gif" alt="(1/3)*(-173434+4015*x)/(-69272+1635*x)"&gt;&amp;nbsp;&amp;nbsp;to 17 digits of accuracy.&amp;nbsp; (1/3)*(-173434+4015*x)/(-69272+1635*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ArtinsConstant.html"&gt;Artin'sConstant&lt;/a&gt;=&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=58336d9b6a0f06119c062f267a37cdae.gif" alt="(2*(449+52*x))/(2141+1664*x)"&gt;&amp;nbsp;&amp;nbsp;to 17 digits of accuracy. (2*(449+52*x))/(2141+1664*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/DottieNumber.html"&gt;Dottie number&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=d7aa7f765ef4a464e511fed555e3eb63.gif" alt="(1/3)*(-9253+198*x)/(-4469+1664*x)"&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy. (1/3)*(-9253+198*x)/(-4469+1664*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/QRSConstant.html"&gt;QRS Constant&lt;/a&gt; = &amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=a3dfbec1295d81d6844da2f6cdf7ed1e.gif" alt="(2/3)*(1927+303*x)/(2165+104*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 16 digits of accuracy. (2/3)*(1927+303*x)/(2165+104*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://oeis.org/A131330"&gt;Decimal expansion the associated QRS constant &lt;/a&gt;.=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=330f45eccac0e8f1965e7883d29151c9.gif" alt="(20*(1874+225*x))/(18278+2799*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; (20*(1874+225*x))/(18278+2799*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/FibonacciFactorialConstant.html"&gt;Fibonacci factorial constant&lt;/a&gt;=&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=82c212a1b75cf652857d942b6ce88a95.gif" alt=" (1/210)*(19567+5556*x)/(77+16*x)"&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy. &amp;nbsp;(1/210)*(19567+5556*x)/(77+16*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LemniscateConstant.html"&gt;The lemniscate constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=14e4160e991a2f2473068409267e8eaf.gif" alt="(2*(13981+2709*x))/(10819+1242*x)"&gt;&amp;nbsp;&amp;nbsp; to 18 digits of accuracy. (2*(13981+2709*x))/(10819+1242*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/MadelungConstants.html"&gt;Madelung Constant(1.747564594...) &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=6a6fb970b11e92b91ac4abb70fa2c0c8.gif" alt="-(1/10)*(292017+8050*x)/(16711+455*x)"&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy.&amp;nbsp; -(1/10)*(292017+8050*x)/(16711+455*x)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;Madelung Constant(1.747564594...) &amp;nbsp;= &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=86e9f6deae7b7dbcd5fe51c6050c4bc7.gif" alt="(5/2)*(1073-572*x)/(-1664+1505*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; (5/2)*(1073-572*x)/(-1664+1505*x)&lt;/p&gt;
&lt;p&gt;Madelung constant =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=63603d76c21267e462ef4a9efe6fef43.gif" alt="-(2*(25687+2007*x))/(29807+117*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; -(2*(25687+2007*x))/(29807+117*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LochsTheorem.html"&gt;Lochs' constant&lt;/a&gt;,=&amp;nbsp; &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=1b3073b06f2f6dd63f606d0ea0e27dae.gif" alt="(-37333+1300*x)/(-4282+185*x)"&gt;&amp;nbsp;to 17 digits of accuracy.&amp;nbsp; (-37333+1300*x)/(-4282+185*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/WallissConstant.html"&gt;Wallis's constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=9fe02b62b2e1e4a80ae0dd6ad4ed9641.gif" alt="(14063+465*x)/(6799-230*x)"&gt;&amp;nbsp;&amp;nbsp;to 16 digits of accuracy.&amp;nbsp; (14063+465*x)/(6799-230*x)&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/GramPoint.html"&gt;The unique point at which the Gram point is equal to its index&lt;/a&gt;.=&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=19c16f7e3e114c03b9bf61aeab3d0c5f.gif" alt=" (1/20)*(10767999-350452*x)/(57+8*x) "&gt; to 14 digits of accuracy.&amp;nbsp;&amp;nbsp;(1/20)*(10767999-350452*x)/(57+8*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/GoldenRatioConjugate.html"&gt;The Golden Ratio Conjugate&lt;/a&gt; =&amp;nbsp; &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=d94b3b054fee7e298fad26c873cdb736.gif" alt="(1/800)*(1080437+25600*x)/(2185+53*x)"&gt;&amp;nbsp; to 20 digits of accuracy.&amp;nbsp; (1/800)*(1080437+25600*x)/(2185+53*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html"&gt;Reciprocal Fibonacci Constant&lt;/a&gt;=&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=5f1ac157238b054dae59dffa8444dc40.gif" alt=" (3/86)*(-39497+936*x)/(-409+4*x)"&gt;&amp;nbsp; to 17 digits of accuracy. &amp;nbsp;(3/86)*(-39497+936*x)/(-409+4*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/LehmersConstant.html"&gt;Lehmer's constant&lt;/a&gt; = &amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=5994b57db9b4fb859976f90273ebe39d.gif" alt="(1/4)*(-7811+328*x)/(-3276+37*x)"&gt;&amp;nbsp;&amp;nbsp; to 17 digits of accuracy. (1/4)*(-7811+328*x)/(-3276+37*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/MillsConstant.htmlhttp://mathworld.wolfram.com/MillsConstant.html"&gt;Mills' constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=f6681bb2fc24290c66c985b89089453f.gif" alt="(423322+19585*x)/(324041+15000*x)"&gt;&amp;nbsp;&amp;nbsp;to 18 digits of accuracy.&amp;nbsp; (423322+19585*x)/(324041+15000*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;Mills' Constant =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=606ae07f30cf26fdeafeae70e196781d.gif" alt="(-1557033+56441*x)/(-1191961+43687*x) "&gt;&amp;nbsp;&amp;nbsp; to 18 D.O.A.&amp;nbsp; &lt;span style="font-family: Calibri; font-size: small;"&gt;(-1557033+56441*x)/(-1191961+43687*x) &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;The real part of &lt;a href="http://www.wolframalpha.com/input/?i=omega-1+constant"&gt;the omega-1 constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=3af36c0a7109f00a8e376d080536f803.gif" alt="(237*(51+2*x))/(15785+702*x)"&gt;&amp;nbsp;&amp;nbsp;to 16 digits of accuracy. (237*(51+2*x))/(15785+702*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/Omega-2Constant.html"&gt;The omega2 Constant&lt;/a&gt; = &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=824aafc70067f45839e5c3133b919058.gif" alt=" (1/16)*(25371-5*x)/(996+215*x)"&gt;&amp;nbsp; to 18 digits of accuracy.&amp;nbsp;&amp;nbsp;&amp;nbsp;(1/16)*(25371-5*x)/(996+215*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 2</description>
      <guid>99867</guid>
      <pubDate>Sun, 05 Dec 2010 09:09:33 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>Page 3:Let x=MRB constant.Tribonacci</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2?ref=Feed:MaplePrimes:MRB constant N part 2:Comments#comment100058</link>
      <itunes:summary>&lt;p&gt;Page 4:&lt;/p&gt;
&lt;p&gt;Let x=MRB constant.&lt;/p&gt;
&lt;p&gt;The digits of accuracy (D.O.A.) might seem embellished by 1 digit because it is computed by the reciprocal of the magnitude of error. For instance, The Champernowne Constant = 0.1234567891011121314151617181920212223243..., and its approximation constructed from the MRB constant is (1/2)*(8647+1490*x)/(31589+24300*x).&amp;nbsp; 0.1234567891011121314151617181920212223243-(1/2)*(8647+1490*x)/(31589+24300*x)= 9.79861545008*10^(-19). Thus, according to this rule,&amp;nbsp;there&amp;nbsp;are 19 digits worth of accuracy in the approximation. However, You could argue that counting the 0, only 18 digits actually match&amp;nbsp;.&lt;/p&gt;
&lt;p&gt;Each approximation is followed by a Maple input of what is written in the pretty print, so you can use Maple to see them for yourself.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/LandauConstant.html"&gt;The upper bound of Landau Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=0b0a6cb37c6b30df408ec0414d7e8fd6.gif" alt="(1/20)*(185372+14133*x)/(17028+1477*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 digits of accuracy. (1/20)*(185372+14133*x)/(17028+1477*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/NaturalLogarithmof2.html"&gt;Log(2) &lt;/a&gt;=&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=a4d34c31f132747305eaac06aa3d56c0.gif" alt="1/75721"&gt;&amp;nbsp;*(&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=7bef35e0ea429db77bf8fdfe3b19f9e9.gif" alt="((90019/10)*Pi+24600-2100*x)"&gt;)&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19&amp;nbsp;D.&amp;nbsp;O. A.. 1/75721*((90019/10)*Pi+24600-2100*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://www.wolframalpha.com/input/?i=Polygon+circumscription+constant"&gt;Polygon circumscription constant&lt;/a&gt;&amp;nbsp;=&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=698487f2fe6fa0bda68cc183b52f3afc.gif" alt=" (2*(-21925+1608*x))/(-381505+28024*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 D.O.A.&amp;nbsp;&amp;nbsp;&amp;nbsp;(2*(-21925+1608*x))/(-381505+28024*x)&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/One-NinthConstant.html"&gt;One-Ninth Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=cab84874c5f9810a55ec8e59472a8ba0.gif" alt="(8/3)*(1314+601*x)/(32759+13768*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 D.O.A&amp;nbsp;&amp;nbsp; (8/3)*(1314+601*x)/(32759+13768*x)&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/TribonacciConstant.html"&gt;Tribonacci Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;a href="http://mathworld.wolfram.com/TribonacciConstant.html"&gt;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=7d657161a8228cfbd5fdcc0c9ff3ec02.gif" alt="(10*(6658+553*x))/(36139+3325*x)"&gt;&lt;/a&gt;&amp;nbsp;&amp;nbsp;to 18&amp;nbsp;D.&amp;nbsp;O. A.. (10*(6658+553*x))/(36139+3325*x)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/Circle-CircleIntersection.html"&gt;The offset at which two unit disks overlap by half each's area&lt;/a&gt; =&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=5f1e11d8f0cfe773d40eb49851cc60d9.gif" alt=" (2*(-80081+4033*x))/(-198246+10049*x) "&gt;&amp;nbsp; to 19 D.O.A..&amp;nbsp;&amp;nbsp;&lt;span style="font-size: small;"&gt; (2*(-80081+4033*x))/(-198246+10049*x) &lt;/span&gt;.&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;The offset at which two unit disks overlap by half each's area =&amp;nbsp; &lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=a75700227e31009f295623477dd462b1.gif" alt="(1/40)*(206581+58200*x)/(6382+1855*x)"&gt;&amp;nbsp; to 18 D.O.A..(1/40)*(206581+58200*x)/(6382+1855*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/SquareLinePicking.html"&gt;Average distance between two points chosen at random in a unit square&lt;/a&gt;..=&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=17b9c2bd1719a48bb1db3fb981ce5d76.gif" alt="(10*(5787+301*x))/(111401+3577*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp; (10*(5787+301*x))/(111401+3577*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LiouvillesConstant.html"&gt;Liouville's Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=100d453b3210d969f547b3a9055aaf00.gif" alt="(15451-259*x)/(138563+7756*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.. (15451-259*x)/(138563+7756*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/GiesekingsConstant.html"&gt;Gieseking's Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=34094eb230b7e331d869b36b92aedb16.gif" alt=" (1/7)*(-624689+21539*x)/(-87927+3029*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 D.O.A&amp;nbsp;&amp;nbsp;&amp;nbsp;(1/7)*(-624689+21539*x)/(-87927+3029*x)&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/UbiquitousConstant.html"&gt;The ubiquitous Constant &lt;/a&gt;=&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=21b8c6147c66854739949c869d101194.gif" alt="(2*(24411+1232*x))/(57643+2821*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A..&amp;nbsp;&lt;span style="font-family: Calibri; font-size: small;"&gt;&amp;nbsp;(2*(24411+1232*x))/(57643+2821*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;a href="http://mathworld.wolfram.com/RabbitConstant.html"&gt;The rabbit Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=f70dc697a5011414b4ddb90da63e5f61.gif" alt="(1/60)*(63631+51200*x)/(1487+1240*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; to 18 D.O.A..&amp;nbsp; &lt;span style="font-family: Calibri; font-size: small;"&gt;(1/60)*(63631+51200*x)/(1487+1240*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size: small;"&gt;&lt;span style="font-family: Calibri;"&gt;&lt;span style="font-family: Calibri; font-size: small;"&gt;&lt;a href="http://mathworld.wolfram.com/PellConstant.html"&gt;Pell Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=d4b819c9fcf2e5dfa125e56395215cc1.gif" alt=" (375*(59+8*x))/(37865+6464*x) "&gt;&amp;nbsp; to 18 D.O.A.&amp;nbsp;&amp;nbsp;&amp;nbsp;(375*(59+8*x))/(37865+6464*x)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ReuleauxTetrahedron.html"&gt;The Reuleaux tetrahedron volume&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=c72fc1ff2480b8478510c883baca7ab0.gif" alt="(4771-1684*x)/(10377+932*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; (4771-1684*x)/(10377+932*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/Copeland-ErdosConstant.html"&gt;Copeland-Erdős Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=4d146554d270f6b2ecf4c0c9cf04d376.gif" alt="(1/3)*(92951+8000*x)/(131783+9528*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp; (1/3)*(92951+8000*x)/(131783+9528*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/WylersConstant.html"&gt;Wyler's Constant &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=ecc2aab148f6de6014e7c6aeb6b243ba.gif" alt="(-593+9*x)/(-82001+5165*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; to 19 D.O.A.&amp;nbsp; (-593+9*x)/(-82001+5165*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/MadelungConstants.html"&gt;The hexagonal Madelung constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=4b0af9f10c1b94f338b91a4e3f89dee2.gif" alt="(8*(1141-68*x))/(1071+2336*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 16 D.O.A.&amp;nbsp; (8*(1141-68*x))/(1071+2336*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://oeis.org/A074071"&gt;Thue constant in base 10&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=1adca5fe1d143646649c0a05e6ea561b.gif" alt="(32*(-37833+1927*x))/(-1409291+72184*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 D.O.A.&amp;nbsp; (32*(-37833+1927*x))/(-1409291+72184*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/TwinPrimesConstant.html"&gt;Twin Primes Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=6ab0767128c26f97c98970a42d60d17d.gif" alt="(1/2)*(-188539+9258*x)/(-142788+6961*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 20 D.O.A.&amp;nbsp; (1/2)*(-188539+9258*x)/(-142788+6961*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/CahensConstant.html"&gt;Cahen's Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=4d40f546b9c7e30ac8c91da0172b9697.gif" alt="(1040*(-339+16*x))/(-548059+26416*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp; (1040*(-339+16*x))/(-548059+26416*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ConwaysConstant.html"&gt;Conway's Constant &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=b6223a6836d5c550090b62c65d587da2.gif" alt="(1/10)*(57511+15930*x)/(4523+630*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; to 18 D.O.A.&amp;nbsp; (1/10)*(57511+15930*x)/(4523+630*x)&lt;/p&gt;
&lt;p&gt;&lt;br&gt;Conway's constant =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=9905edad11bb1332d3fcbba95409a5ac.gif" alt="(10*(13066+9559*x))/(95399+99055*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 21 D.O.A.&amp;nbsp; (10*(13066+9559*x))/(95399+99055*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/PrimeConstant.html"&gt;The prime constant in base 10&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=98cea0b1b692bd4e700ce8d76570fc6d.gif" alt=" (9/20)*(5334+817*x)/(5779+936*x)"&gt;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp;&amp;nbsp;&amp;nbsp;(9/20)*(5334+817*x)/(5779+936*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://oeis.org/A093064"&gt;The mean line-in-equilateral triangle length&lt;/a&gt; (i.e.0.3647918433...) =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=0e1b1675f13bbc7047e357c64f6147e6.gif" alt="(4*(3319+570*x))/(35997+8360*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A..&amp;nbsp; (4*(3319+570*x))/(35997+8360*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ChampernowneConstant.html"&gt;Champernowne Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=0f80712a1def9c6813f7a49480a23f91.gif" alt="(1/2)*(8647+1490*x)/(31589+24300*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 digits of accuracy.&amp;nbsp; (1/2)*(8647+1490*x)/(31589+24300*x)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 2</description>
      <guid>100058</guid>
      <pubDate>Fri, 10 Dec 2010 05:37:43 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>&amp;nbsp;&amp;nbsp;Page 5:Let x=MRB constant.The</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2?ref=Feed:MaplePrimes:MRB constant N part 2:Comments#comment100295</link>
      <itunes:summary>&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&lt;span&gt;&amp;nbsp;
&lt;p&gt;Page 5:&lt;/p&gt;
&lt;p&gt;Let x=MRB constant.&lt;/p&gt;
&lt;p&gt;The digits of accuracy (D.O.A.) might seem embellished by 1 digit because it is computed by the reciprocal of the magnitude of error. For instance, The Champernowne Constant = 0.1234567891011121314151617181920212223243..., and its approximation constructed from the MRB constant is (1/2)*(8647+1490*x)/(31589+24300*x).&amp;nbsp; 0.1234567891011121314151617181920212223243-(1/2)*(8647+1490*x)/(31589+24300*x)= 9.79861545008*10^(-19). Thus, according to this rule,&amp;nbsp;there&amp;nbsp;are 19 digits worth of accuracy in the approximation. However, You could argue that counting the 0, only 18 digits actually match&amp;nbsp;.&lt;/p&gt;
&lt;p&gt;Each approximation is followed by a Maple input of what is written in the pretty print, so you can use Maple to see them for yourself.&lt;/p&gt;
&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/SierpinskiConstant.html"&gt;Sierpiński Constant &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=7bca7ee7d066eda61e892a6d8ab74557.gif" alt="(-7652+81*x)/(-9550+1431*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; (-7652+81*x)/(-9550+1431*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/DominoTiling.html"&gt;The dimer&amp;nbsp;constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=6e794ee369f5821fa294ce54773e4f7c.gif" alt="(8*(3412+5*x))/(14629+3250*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 18 D.O.A.&amp;nbsp; (8*(3412+5*x))/(14629+3250*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/HardHexagonEntropyConstant.html"&gt;Hard Hexagon Entropy Constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=9907420cd1123d0a27574127d4bd7771.gif" alt="(10*(-691+61*x))/(-5033+870*x) "&gt;&amp;nbsp; to 16 D.O.A.&amp;nbsp; (10*(-691+61*x))/(-5033+870*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/LehmersMahlerMeasureProblem.html"&gt;Lehmer's minimal Mahler Measure Constant &lt;/a&gt;(i.e. 1.17628...) =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=65f42c4153e949521068ddf9d5ed4b4f.gif" alt="(6*(-1729+360*x))/(-8941+2484*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 17 D.O.A.&amp;nbsp; (6*(-1729+360*x))/(-8941+2484*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/CubeTetrahedronPicking.html"&gt;The mean Cube in Tetrahedron volume &lt;/a&gt;=&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=85759d4b757eec81daf3aeb1f2d9edba.gif" alt="(30*(389+15*x))/(838403+57186*x)"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;to 19 D.O.A&amp;nbsp; (30*(389+15*x))/(838403+57186*x)&lt;/p&gt;
&lt;p&gt;&lt;a href="http://mathworld.wolfram.com/ParisConstant.html"&gt;Paris constant&lt;/a&gt; =&amp;nbsp;&amp;nbsp;&lt;img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=151a5301ad99bbed1818565810bf0d65.gif" alt="(10/9)*(-4547+286*x)/(-4567+121*x) "&gt;&amp;nbsp;&amp;nbsp; to 18 D.O.A.&amp;nbsp; (10/9)*(-4547+286*x)/(-4567+121*x)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 2</description>
      <guid>100295</guid>
      <pubDate>Sat, 18 Dec 2010 09:31:28 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
    </item>
    <item>
      <title>This post is continued in the MRB constant</title>
      <link>http://www.mapleprimes.com/posts/99773-MRB-Constant-N-Part-2?ref=Feed:MaplePrimes:MRB constant N part 2:Comments#comment134389</link>
      <itunes:summary>&lt;p&gt;This post is continued in the &lt;a href="http://www.mapleprimes.com/posts/134388-MRB-Constant-N-Part-3?rid=437372"&gt;MRB constant N Part 3&lt;/a&gt;.&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, MRB constant N part 2</description>
      <guid>134389</guid>
      <pubDate>Mon, 21 May 2012 05:38:50 Z</pubDate>
      <itunes:author>Marvin Ray Burns</itunes:author>
      <author>Marvin Ray Burns</author>
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