Number Spiral | Clipmarks


	Number Spiral

JohnWaterman

4-1-2008 4:31 PM

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4 Comments |

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4-1-2008 5:16 PM

alanocu

that is really incredible!

4-2-2008 12:28 AM

Deepti

cool!

4-2-2008 10:37 AM

AcesLucky

Wow. The human mind is fairly good at finding patterns even in the most apparently random of forms. Innovative.

4-2-2008 10:42 AM

skwirlinator

I recall playing with these in math class in high school. Thanks for the forgotten memory reminder.

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<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://www.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/1c3230af-eb5c-4dd1-920f-0c6371faf3a6/98455296-4494-4425-8305-6C5DEC8486FE/" 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://www.numberspiral.com/" href="http://www.numberspiral.com/" style="font-size: 11px;">www.numberspiral.com</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><SPAN class="head">1.  Introduction</SPAN></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><table background="undefined" bgcolor=""><tr><TD><P class="body">Number spirals are very simple. To make one, we just write the non-negative integers on a ribbon and roll it up with zero at the center. </p> <P class="body">The trick is to arrange the spiral so all the perfect squares (1, 4, 9, 16, etc.) line up in a row on the right side:</P></TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.numberspiral.com/img/55D0AA14-A4AB-4A5C-B3DB-E772D0A1EB39" alt="Number wheel, figure 1" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><P>If we continue winding for a while and zoom out a bit, the result looks like this:</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.numberspiral.com/img/055F5C08-1A1C-4BA2-9147-14C114B81EE1" alt="Number wheel, figure 1" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><table background="undefined" bgcolor=""><tr><TD>If we zoom out even further and remove everything except the dots that indicate the locations of integers, we get the next illustration. It shows 2026 dots:</TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.numberspiral.com/img/02E131EB-BE54-456F-9599-274B10BE3B49" alt="Number wheel, figure 2" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><table background="undefined" bgcolor=""><tr><TD>Let's try making the primes darker than the non-primes: </TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/www.numberspiral.com/img/C3A38B97-0404-4D8C-A459-E15247F8F174" alt="Number wheel, figure 2" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><table background="undefined" bgcolor=""><tr><TD>The primes seem to cluster along certain curves. Let's zoom out even further to get a better look. The following number spiral shows all the primes that occur within the first 46,656 non-negative integers. (For clarity, non-primes have been left out.) </TD></tr></table></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.numberspiral.com/img/60CD40CC-A41F-4B30-A2A1-C809156F02BE" alt="Number wheel, figure 2" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.numberspiral.com/">On the next few pages of this website, we'll investigate these patterns and try to make sense out of them</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/98455296-4494-4425-8305-6C5DEC8486FE/blog/" title="blog or email this clip"><img src="http://content7.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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