Logarithmic Spirals

[Boris_Badenov]

<p><font size="3" color="#ff0000">This is from a recent APOD;</font></p><p><font color="#000000"><font size="2"><strong>Image Credit: </strong>M101 - </font></font><font size="2" color="#000000">NASA</font><font size="2" color="#000000">, </font><font size="2" color="#000000">ESA</font><font size="2" color="#000000">, </font><font size="2" color="#000000">CFHT</font><font size="2" color="#000000">, </font><font size="2" color="#000000">NOAO</font><font size="2" color="#000000">; Typhoon Rammasun - </font><font size="2" color="#000000">MODIS</font><font size="2" color="#000000">, </font><font size="2" color="#000000">NASA</font><font size="2" color="#000000"> <br />Comparison: Lawrence Anderson-Huang (</font><font size="2" color="#000000">Ritter Astrophysical Obs.</font><font size="2" color="#000000">, Univ. Toledo) </font></p><p><font size="2" color="#000000">Explanation: Uncomfortably close </font><font size="2" color="#000000">Typhoon Rammasun</font><font size="2" color="#000000"> (right) and 25 million light-year distant </font><font size="2" color="#000000">galaxy M101</font><font size="2" color="#000000"> don't seem to have much in common. For starters, Rammasun was only a thousand kilometers or so across while M101 (aka the Pinwheel Galaxy) spans about 170,000 light-years, making them vastly dissimilar in scale, not to mention the different physical environments that control their </font><font size="2" color="#000000">formation</font><font size="2" color="#000000"> and </font><font size="2" color="#000000">development</font><font size="2" color="#000000">. But they do look amazingly alike: each with arms exhibiting the shape of a simple and beautiful mathematical curve known as a </font><font size="2" color="#000000">logarithmic spiral</font><font size="2" color="#000000">, a spiral whose separation grows in a </font><font size="2" color="#000000">geometric</font><font size="2" color="#000000"> way with increasing distance from the center. Also known as the </font><font size="2" color="#000000">equiangular spiral</font><font size="2" color="#000000">, growth spiral, and Bernoulli's spiral or </font><font size="2" color="#000000">spira mirabilis</font><font size="2" color="#000000">, this curve's </font><font size="2" color="#000000">rich properties</font><font size="2" color="#000000"> have fascinated </font><font size="2" color="#000000">mathematicians</font><font size="2" color="#000000"> since its discovery by 17th century philosopher </font><font size="2" color="#000000">Descartes</font><font size="2" color="#000000">. Intriguingly, this abstract shape is much more abundant in nature than suggested by the striking visual comparison above. For example, logarithmic spirals can also describe the tracks of subatomic particles in a </font><font size="2" color="#000000">bubble chamber</font><font size="2" color="#000000">, the arrangement of </font><font size="2" color="#000000">sunflower seeds</font><font size="2" color="#000000"> and, of course, </font><font size="2" color="#000000">cauliflower</font><font size="2" color="#000000">. <br /></font></p><p>&nbsp;</p><p>http://antwrp.gsfc.nasa.gov:80/apod/image/0805/NaturalSpirals.jpg</p> <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

 

[starsinmyeyes44]

<p>&nbsp;they do look amazingly alike: each with arms exhibiting the shape of a simple and beautiful mathematical curve known as a logarithmic spiral, a spiral whose separation grows in a geometric way with increasing distance from the center.Posted by boris1961[/QUOTE]</p><p>&nbsp;</p><p><font size="2" color="#0000ff">Very cool pictures!&nbsp; It would be neat to see a "smallest to largest" photo collage of examples of logarithmic spirals.</font></p> <div class="Discussion_UserSignature"> <p><font color="#ff00ff">In the book of life, the answers aren't in the back.<br /></font><strong>Charlie Brown</strong></p> </div>