<div dir="ltr"><div class="gmail_default" style="font-family:comic sans ms,sans-serif;font-size:large;color:#000000">Pretty cool, but you are plainly not a gardener. Do you think that the early people did architecture according to the Golden Rectangle without knowing what they were doing and finally someone figured out the geometry? </div><div class="gmail_default" style="font-family:comic sans ms,sans-serif;font-size:large;color:#000000"><br></div><div class="gmail_default" style="font-family:comic sans ms,sans-serif;font-size:large;color:#000000">Why do I keep asking questions when it is clear that I will not understand the answers? Take an accordion: as you pull it apart the pleats start disappearing, just as if you could pull a wavy wall to make it a straight wall. How can it be? Straightening out the pleats makes it longer with the same number of pleats. ???? bill w</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Aug 1, 2022 at 2:19 PM spike jones via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">extropy-chat@lists.extropy.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div lang="EN-US" style="overflow-wrap: break-word;"><div class="gmail-m_1116121287234146855WordSection1"><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><div><div style="border-right:none;border-bottom:none;border-left:none;border-top:1pt solid rgb(225,225,225);padding:3pt 0in 0in"><p class="MsoNormal"><b>From:</b> <a href="mailto:spike@rainier66.com" target="_blank">spike@rainier66.com</a> <<a href="mailto:spike@rainier66.com" target="_blank">spike@rainier66.com</a>> <br><b>…<u></u><u></u></b></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal">>… grassy area on the right is a golden ratio ellipse…<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal">>…We math geeks build stuff like this… spike<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><img width="400" height="338" style="width: 4.1666in; height: 3.5208in;" id="gmail-m_1116121287234146855Picture_x0020_2" src="cid:1825f48ff186917eb1"><u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></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.<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></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. <u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></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.<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></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.<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal">This yard is a puzzling blend of Greek and Zen, with lotsa math geek chic holding it all together.<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal">spike<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><u></u> <u></u></p></div></div></div></div>_______________________________________________<br>
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