The Golden ratio | Clipmarks


	The Golden ratio
rj3sp
4-5-2008 6:08 PM
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golden ratio
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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://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/e92a08f8-bce2-4487-9b21-84040b065e1f/B04D4D69-F341-4697-BF2F-0EDF6D178BE4/" 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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319" href="http://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319" style="font-size: 11px;">en.wikipedia.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><SPAN>Golden ratio</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/en.wikipedia.org/img/22EDAC77-42C1-423C-A885-1F06CBFB136A" alt="The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
<DIV class="magnify"><A title="Enlarge" class="internal" href="http://en.wikipedia.org/wiki/Image:Golden_ratio_line.svg"><IMG width="15" height="11" alt="" src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" /></A></DIV>
The <B>golden section</B> is a line segment sectioned into two according to the <B>golden ratio</B>. The total length <FONT color="green"><I><B>a+b</B></I></FONT> is to the longer segment <FONT color="blue"><I><B>a</B></I></FONT> as <FONT color="blue"><I><B>a</B></I></FONT> is to the shorter segment <FONT color="red"><I><B>b</B></I></FONT>.</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/en.wikipedia.org/img/E3853418-5FAF-48CA-9757-245196915F40" alt="Leonardo Da Vinci's illustration from De Divina Proportione applies geometric proportions to the human face." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
<DIV class="magnify"><A title="Enlarge" class="internal" href="http://en.wikipedia.org/wiki/Image:Divina_proportione.png"><IMG width="15" height="11" alt="" src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" /></A></DIV>
Leonardo Da Vinci's illustration from <I>De Divina Proportione</I> applies geometric proportions to the human face.</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/en.wikipedia.org/img/259B7610-A1A7-41AF-81F0-9AC8789D93BD" alt="A pentagram colored to distinguish its line segments of different lengths. The four lengths are in golden ratio to one another." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
<DIV class="magnify"><A title="Enlarge" class="internal" href="http://en.wikipedia.org/wiki/Image:Pentagram-phi.svg"><IMG width="15" height="11" alt="" src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" /></A></DIV>
A pentagram colored to distinguish its line segments of different lengths. The four lengths are in <STRONG class="selflink">golden ratio</STRONG> to one another.</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/en.wikipedia.org/img/F72FA47A-CD1E-4C17-8D24-466651C8E1FF" alt="A Fibonacci spiral that approximates the golden spiral, using Fibonacci sequence square sizes up to 34." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
<DIV class="magnify"><A title="Enlarge" class="internal" href="http://en.wikipedia.org/wiki/Image:Fibonacci_spiral_34.svg"><IMG width="15" height="11" alt="" src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" /></A></DIV>
A <A title="Fibonacci sequence" class="mw-redirect" href="http://en.wikipedia.org/wiki/Fibonacci_sequence">Fibonacci spiral</A> that approximates the golden spiral, using Fibonacci sequence square sizes up to 34.</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/en.wikipedia.org/img/553AEDD9-FA40-4758-A69F-3E47DA487A3E" alt="A regular square pyramid is determined by its medial right triangle, whose edges are the pyramid's apothem (a), semi-base (b), and height (h); the face inclination angle is also marked.  Mathematical proportions b:h:a of  and  and  are of particular interest in relation to Egyptian pyramids." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
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A regular square pyramid is determined by its medial right triangle, whose edges are the pyramid's apothem (a), semi-base (b), and height (h); the face inclination angle is also marked. Mathematical proportions b:h:a of <IMG src="http://upload.wikimedia.org/math/0/7/a/07a657258ba554dafc3ca8a7505a2b7b.png" alt="1:\sqrt{\varphi}:\varphi" class="tex" /> and <IMG src="http://upload.wikimedia.org/math/2/5/3/253f1ac21faf86ab8306d4dc4826b893.png" alt="3:4:5\ " class="tex" /> and <IMG src="http://upload.wikimedia.org/math/4/e/2/4e22fa5368136f402425d5d90f8837f1.png" alt="1:4/\pi:1.61899\ " class="tex" /> are of particular interest in relation to Egyptian pyramids.</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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/en.wikipedia.org/img/14611F72-AC10-4107-B548-9F77C62A1F70" alt="The sculpture Ratio by Andrew Rogers in Jerusalem is proportioned according to Fibonacci numbers; some call it Golden Ratio." /></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://en.wikipedia.org/w/index.php?title=Golden_ratio&oldid=203126319"><DIV class="thumbcaption">
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The sculpture <I>Ratio</I> by Andrew Rogers in Jerusalem is proportioned according to Fibonacci numbers; some call it <I>Golden Ratio</I>.</DIV></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/B04D4D69-F341-4697-BF2F-0EDF6D178BE4/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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