<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=utf-8"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle19
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> spike@rainier66.com <spike@rainier66.com> <br><b>…<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>>… grassy area on the right is a golden ratio ellipse…<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>>…We math geeks build stuff like this… spike<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><img width=400 height=338 style='width:4.1666in;height:3.5208in' id="Picture_x0020_2" src="cid:image003.jpg@01D8A5A0.A1484C90"><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Billw, since you are burning with curiosity about golden ratio ellipses (or if not, you are the kind of gentlemanly sort to play along politely) this is the front yard of me ‘umble abode.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The five steps down are golden ratio ellipses with a minor radius of 1 meter. The major radius of those steps ((1+5^.5)/2) meters, is the minor radius of the tan bark region to the left of the steps. The major radius of that ellipse is the minor radius of the back yard grassy ellipse, and the major radius of the grassy ellipse is the minor radius of the ellipse toward the left side forward quadrant of the photo. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>It isn’t clear from this photo, but the inflection point between the tangent ellipses was placed right were the first derivative on each of the ellipses was equal, so it is a continuous first derivative over the transition from one ellipse to the other.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>But wait, there’s more. I had more time on my hands then, being in my 30s, pre-child, part-time job only. I worked a 9 to 5 at Lockheed Martin but 40 hrs a week is considered a part time job by Silicon Valley standards. I had to figure out a way to generate the ellipses in order to build the form walls for the cement. So… I used surveying tools to figure out exactly where to drive the focus stakes on which I attached the cable to generate the ellipses.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>This yard is a puzzling blend of Greek and Zen, with lotsa math geek chic holding it all together.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>spike<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></div></div></body></html>