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<div class=3DSection1>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><span style=3D'font-size:36.0pt'>MRB Constant<o:p></o:p></span></b>=
</p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
style=3D'font-size:36.0pt'>By Marvin Ray Burns<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:36.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:48.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:48.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:48.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Consider this sequence of n-cubes:</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

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,<!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=3D82 height=3D97
src=3D"what_is_mrb_files/image020.jpg" v:shapes=3D"_x0000_i1030"><![endif]>,
&#8230; ,<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span><!--[if mso &=
 !supportInlineShapes & supportFields]><span
style=3D'mso-element:field-begin;mso-field-lock:yes'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>SHAPE<span
style=3D'mso-spacerun:yes'>&nbsp; </span>\* MERGEFORMAT <span style=3D'mso-=
element:
field-separator'></span><![endif]--><!--[if gte vml 1]><v:oval id=3D"_x0000=
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<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:20.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'>Give each element a conten=
t equal
to its dimension.<sup> [0]</sup></p>

<p class=3DMsoNormal style=3D'margin-left:.25in;mso-layout-grid-align:none;
text-autospace:none'>In the <span class=3DSpellE>y<span class=3DGramE>,z</s=
pan></span>-plane
in 3d space, line up vertically the edge of the Line Segment at the origin =
down
the z-axis; it stops at the point (0,0,-1). So at the point (0<span
class=3DGramE>,1</span>,-1) line up an edge of the square so that it stops =
at the
point (0,1,-1+sqrt[2]). So at the point (0,2,-1+2^(1/2)) line up an edge of=
 the
cube so that it stops at (0,2,-1+2^(1/2)-3^(1/3). Continue stacking an edge=
 of
every hypercube <i style=3D'mso-bidi-font-style:normal'>until you get to th=
e cube
of infinite dimension; it starts at the <span class=3DGramE>point</span></i=
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style=3D'mso-bidi-font-style:normal'><span style=3D'mso-element:field-begin=
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EQ </i><![endif]--><!--[if supportFields]><i style=3D'mso-bidi-font-style:n=
ormal'><span
style=3D'mso-element:field-end'></span></i><![endif]--><!--[if supportField=
s]><i
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ields]><i
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</xml><![endif]-->(0,</i><i style=3D'mso-bidi-font-style:normal'><span
style=3D'font-family:"Bookman Old Style"'>&#8734;</span>,-m) so that it sto=
ps at
the point (0,</i><i style=3D'mso-bidi-font-style:normal'><span style=3D'fon=
t-family:
"Bookman Old Style"'>&#8734;</span>,m) where m is the MRB constant.<o:p></o=
:p></i></p>

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pan
style=3D'color:black'><span style=3D'mso-element:field-begin;mso-field-lock=
:yes'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>SHAPE<span
style=3D'mso-spacerun:yes'>&nbsp; </span>\* MERGEFORMAT <span style=3D'mso-=
element:
field-separator'></span></span><![endif]--><span style=3D'color:black'><!--=
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pt;
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d">
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96">
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:6.0pt'>Cube<o:p></o:p></span></p>
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rom=3D"3290,5737"
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1,5737"
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 to=3D"3895,10132"
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3,5706"
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lor=3D"blue">
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rom=3D"4515,5801"
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 to=3D"4727,9988"
  strokecolor=3D"blue"/>
 <v:line id=3D"_x0000_s1064" style=3D'position:absolute;flip:y' from=3D"493=
6,5861"
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5163,5864"
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om=3D"8433,6285"
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 <v:shape id=3D"_x0000_s1069" type=3D"#_x0000_t202" style=3D'position:absol=
ute;
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>=
<span
     style=3D'font-size:13.5pt;mso-bidi-font-size:12.0pt'>m</span></span><s=
pan
     style=3D'font-size:13.5pt;mso-bidi-font-size:12.0pt'><o:p></o:p></span=
></p>
     </div>
     <![if !mso]></td>
    </tr>
   </table>
   <![endif]></v:textbox>
 </v:shape><v:shape id=3D"_x0000_s1070" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
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  strokecolor=3D"#396">
  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Line
     Segment<o:p></o:p></span></p>
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     <![if !mso]></td>
    </tr>
   </table>
   <![endif]></v:textbox>
 </v:shape><v:shape id=3D"_x0000_s1071" style=3D'position:absolute;left:398=
3;top:10268;
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,e"
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  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
 </v:shape><v:shape id=3D"_x0000_s1072" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
  left:3531;top:11304;width:900;height:402' filled=3D"f" stroked=3D"f"
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Penteract<o:p></o:p></span></p>
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     <![if !mso]></td>
    </tr>
   </table>
   <![endif]></v:textbox>
 </v:shape><v:shape id=3D"_x0000_s1073" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Hepteract<o:p></o:p></span></p>
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    </tr>
   </table>
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tion:absolute;
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
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     <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
     style=3D'font-size:7.0pt;mso-bidi-font-size:6.0pt'>Hexeract<o:p></o:p>=
</span></p>
     <p class=3DMsoNormal><span style=3D'font-size:13.5pt;mso-bidi-font-siz=
e:12.0pt'><o:p>&nbsp;</o:p></span></p>
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    </tr>
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tion:absolute;
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6">
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   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Octeract</span><span
     style=3D'font-size:13.5pt;mso-bidi-font-size:12.0pt'><o:p></o:p></span=
></p>
     </div>
     <![if !mso]></td>
    </tr>
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3;top:4575;
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0e"
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  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
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tion:absolute;
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   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
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     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>10-cube<o:p></o:p></span></p>
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8428,5781"
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d=3D"f"
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3;top:10343;
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5;top:10223;
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7;top:4590;
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d=3D"f"
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0;top:4665;
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d=3D"f"
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   <v:f eqn=3D"min #1 @6"/>
   <v:f eqn=3D"prod @7 1 2"/>
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    <tr>
     <td><![endif]>
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     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Square<o:p></o:p></span></p>
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    </tr>
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 </v:shape><v:shape id=3D"_x0000_s1122" style=3D'position:absolute;left:280=
5;top:4590;
  width:630;height:1080' coordsize=3D"630,1080" path=3D"m,l630,1080e"
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  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
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tion:absolute;
  left:3015;top:4284;width:967;height:403' filled=3D"f" fillcolor=3D"silver"
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
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   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Tesseract<o:p></o:p></span></p>
     <p class=3DMsoNormal><span style=3D'font-size:13.5pt;mso-bidi-font-siz=
e:12.0pt'><o:p>&nbsp;</o:p></span></p>
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    </tr>
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3;top:4575;
  width:285;height:938' coordsize=3D"285,938" path=3D"m,l285,938e" strokeco=
lor=3D"blue">
  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
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5;top:10095;
  width:315;height:1245;mso-position-horizontal:absolute;
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,e"
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  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
 </v:shape><v:shape id=3D"_x0000_s1126" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
  left:4995;top:11304;width:900;height:403' filled=3D"f" stroked=3D"f"
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  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
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   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Enneract<o:p></o:p></span></p>
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    </tr>
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 </v:shape><v:shape id=3D"_x0000_s1139" style=3D'position:absolute;left:843=
0;top:9645;
  width:1;height:1273;mso-position-horizontal:absolute;mso-position-vertica=
l:absolute'
  coordsize=3D"1,1273" path=3D"m,1273l,e" filled=3D"f" strokecolor=3D"blue">
  <v:stroke dashstyle=3D"dash"/>
  <v:path arrowok=3D"t"/>
 </v:shape><v:shape id=3D"_x0000_s1140" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
  left:7425;top:10944;width:1980;height:403' filled=3D"f" stroked=3D"f"
  strokecolor=3D"#396">
  <v:textbox inset=3D"2.85369mm,1.42683mm,2.85369mm,1.42683mm">
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span style=3D'font-size:7.0pt;mso-bidi-font-size=
:6.0pt'>Cube
     of infinite dimension<o:p></o:p></span></p>
     </div>
     <![if !mso]></td>
    </tr>
   </table>
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;top:5724;
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5,5724"
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  <v:stroke endarrow=3D"open"/>
 </v:line><v:shape id=3D"_x0000_s1159" type=3D"#_x0000_t202" style=3D'posit=
ion:absolute;
  left:3015;top:4584;width:540;height:360' stroked=3D"f">
  <v:textbox>
   <![if !mso]>
   <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
    <tr>
     <td><![endif]>
     <div>
     <p class=3DMsoNormal><span class=3DGramE>z</span></p>
     </div>
     <![if !mso]></td>
    </tr>
   </table>
   <![endif]></v:textbox>
 </v:shape><v:shape id=3D"_x0000_s1160" type=3D"#_x0000_t202" style=3D'posi=
tion:absolute;
  left:6795;top:5444;width:1260;height:540' stroked=3D"f">
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<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><sup><o:p>&nbsp;</o:p></sup></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup>[0]<o:p></o:p></sup></=
p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><a
href=3D"http://www23.wolframalpha.com/input/?i=3Dn-cube">http://www23.wolfr=
amalpha.com/input/?i=3Dn-cube</a><o:p></o:p></sup></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup><o:p>&nbsp;</o:p></sup=
></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><sup>1</sup><a
href=3D"http://pi.lacim.uqam.ca/fra/table_fr.html">http://pi.lacim.uqam.ca/=
fra/table_fr.html</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://pi.lacim.uqam.ca/eng/table_en.html">http://pi.lacim.uqam.ca/=
eng/table_en.html</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://www.irancivilcenter.com/en/tools/units/math_const.php">http:=
//www.irancivilcenter.com/en/tools/units/math_const.php</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://www.wortherkunft.de/~e/c_/ca-zahlen.html">http://www.worther=
kunft.de/~e/c_/ca-zahlen.html</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://free-vz.htnet.hr/nstepan/const/math.txt">http://free-vz.htne=
t.hr/nstepan/const/math.txt</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://pi.lacim.uqam.ca/piDATA/mrburns.txt">http://pi.lacim.uqam.ca=
/piDATA/mrburns.txt</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><a
href=3D"http://www.research.att.com/~njas/sequences/A037077">http://www.res=
earch.att.com/~njas/sequences/A037077</a></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><span
class=3DMathematicaFormatStandardForm>S. R. Finch, Mathematical Constants, =
<st1:place
w:st=3D"on"><st1:City w:st=3D"on">Cambridge</st1:City></st1:place>, 2003, p=
p.
448-452.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'margin-left:.5in'><o:p>&nbsp;</o:p></p>

</div>

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