<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/3c6d9421-89ee-49d0-8284-be005c2b8d8e/42A3D7F2-989F-41AB-B469-A9ED1110E081/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html" href="http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html" style="font-size: 11px;">mathworld.wolfram.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html"><DIV align="center"><IMG width="425" height="67" alt="Tupper%27s%20formula" src="http://mathworld.wolfram.com/images/gifs/TuppersFormula.gif" /> </DIV> <P class="Text"> J. Tupper concocted the amazing formula </p> <DIV> <TABLE width="100%" cellspacing="0" cellpadding="0" align="center"><TBODY><TR><TD align="left"><IMG width="233" height="35" alt="1/2%3C%7C_mod%28%7C_y/%2817%29_%7C2%5E%28-17%7C_x_%7C-mod%28%7C_y_%7C%2C17%29%29%2C2%29_%7C%2C" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/equation1.gif" /></TD></TR></TBODY></TABLE></DIV> <P class="Text"> where <IMG width="18" height="15" border="0" alt="%7C_x_%7C" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/inline1.gif" /> is the <A class="Hyperlink" href="http://mathworld.wolfram.com/FloorFunction.html">floor function</A> and <IMG width="61" height="15" border="0" alt="mod%28b%2Cm%29" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/inline2.gif" /> is the <A class="Hyperlink" href="http://mathworld.wolfram.com/Mod.html" set="yes">mod</A> function, which, when graphed over <IMG width="69" height="15" border="0" alt="0%3C=x%3C=105" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/inline3.gif" /> and <IMG width="84" height="15" border="0" alt="n%3C=y%3C=n+16" class="inlineformula" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/inline4.gif" /> with </p> <DIV> <TABLE width="100%" cellspacing="0" cellpadding="0" align="center"><TBODY><TR><TD align="left"><IMG width="526" height="283" alt="n==960939379918958884971672962127852754715004339660129306651505519271702802395266%20%0A424689642842174350718121267153782770623355993237280874144307891325963941337723%20%0A487857735749823926629715517173716995165232890538221612403238855866184013235585%20%0A136048828693337902491454229288667081096184496091705183454067827731551705405381%20%0A627380967602565625016981482083418783163849115590225610003652351370343874461848%20%0A378737238198224849863465033159410054974700593138339226497249461751545728366702%20%0A369745461014655997933798537483143786841806593422227898388722980000748404719%2C%20" src="http://mathworld.wolfram.com/images/equations/TuppersSelf-ReferentialFormula/equation2.gif" /></TD></TR></TBODY></TABLE></DIV> <P class="Text"> gives the self-referential "plot" illustrated above.</P></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/42A3D7F2-989F-41AB-B469-A9ED1110E081/blog/" title="blog or email this clip"><img src="http://content6.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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