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	Comments on: Geometric constructions of Phi in Circles	</title>
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	<link>https://www.goldennumber.net/circles/</link>
	<description>Golden Ratio, Phi, 1.618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face. One source with over 100 articles and latest findings.</description>
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	<item>
		<title>
		By: kg		</title>
		<link>https://www.goldennumber.net/circles/#comment-6412</link>

		<dc:creator><![CDATA[kg]]></dc:creator>
		<pubDate>Sat, 02 Apr 2022 12:52:02 +0000</pubDate>
		<guid isPermaLink="false">http://www.phisource.com/?p=386#comment-6412</guid>

					<description><![CDATA[holy (blank)!]]></description>
			<content:encoded><![CDATA[<p>holy (blank)!</p>
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		<title>
		By: Rodolfo		</title>
		<link>https://www.goldennumber.net/circles/#comment-6162</link>

		<dc:creator><![CDATA[Rodolfo]]></dc:creator>
		<pubDate>Wed, 11 Aug 2021 21:10:07 +0000</pubDate>
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					<description><![CDATA[In reply to &lt;a href=&quot;https://www.goldennumber.net/circles/#comment-266&quot;&gt;Gary Meisner&lt;/a&gt;.

Credo che il cerchio sia già la dimostrazione di ciò che hai detto. 
Il cerchio, come parte misurabile, può esistere solo grazie ad un punto detto centro, non misurabile.

I believe the circle is already proof of what you said. The circle, as a measurable part, can exist only thanks to a point called the center, which is not measurable.]]></description>
			<content:encoded><![CDATA[<p>In reply to <a href="https://www.goldennumber.net/circles/#comment-266">Gary Meisner</a>.</p>
<p>Credo che il cerchio sia già la dimostrazione di ciò che hai detto.<br />
Il cerchio, come parte misurabile, può esistere solo grazie ad un punto detto centro, non misurabile.</p>
<p>I believe the circle is already proof of what you said. The circle, as a measurable part, can exist only thanks to a point called the center, which is not measurable.</p>
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		<title>
		By: Rodolfo		</title>
		<link>https://www.goldennumber.net/circles/#comment-6161</link>

		<dc:creator><![CDATA[Rodolfo]]></dc:creator>
		<pubDate>Wed, 11 Aug 2021 20:54:40 +0000</pubDate>
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					<description><![CDATA[Non so se sia pertinente al meraviglioso tema trattato, volevo condividere una considerazione nata dalla contemplazione del cerchio e dalla sua definizione geometrica. &quot; L&#039;insieme dei punti equidistanti da un punto detto centro &quot;
L&#039;insieme dei punti appartengono al Regno del misurabile, quindi materiale. 
Ma questo insieme non può esistere senza la sua origine , cioè quel Punto  detto centro , non misurabile, quindi non materiale. 
Mi sembra quasi una dimostrazione matematica che la materia (il mondo conosciuto) possa esistere solo grazie alla non materia o spirito. Forse non nell&#039;uno ma nello zero la vera natura divina.

I do not know if it is pertinent to the wonderful subject dealt with, I wanted to share a consideration born from the contemplation of the circle and its geometric definition. &quot;The set of points equidistant from a point called the center&quot;. The set of points belong to the realm of the measurable, therefore material. But this set cannot exist without its origin, that is, that Point called the center, which is not measurable and therefore not material. It seems to me almost a mathematical demonstration that matter (the known world) can exist only thanks to non-matter or spirit. Perhaps not in the one but in the zero the true divine nature.]]></description>
			<content:encoded><![CDATA[<p>Non so se sia pertinente al meraviglioso tema trattato, volevo condividere una considerazione nata dalla contemplazione del cerchio e dalla sua definizione geometrica. &#8221; L&#8217;insieme dei punti equidistanti da un punto detto centro &#8221;<br />
L&#8217;insieme dei punti appartengono al Regno del misurabile, quindi materiale.<br />
Ma questo insieme non può esistere senza la sua origine , cioè quel Punto  detto centro , non misurabile, quindi non materiale.<br />
Mi sembra quasi una dimostrazione matematica che la materia (il mondo conosciuto) possa esistere solo grazie alla non materia o spirito. Forse non nell&#8217;uno ma nello zero la vera natura divina.</p>
<p>I do not know if it is pertinent to the wonderful subject dealt with, I wanted to share a consideration born from the contemplation of the circle and its geometric definition. &#8220;The set of points equidistant from a point called the center&#8221;. The set of points belong to the realm of the measurable, therefore material. But this set cannot exist without its origin, that is, that Point called the center, which is not measurable and therefore not material. It seems to me almost a mathematical demonstration that matter (the known world) can exist only thanks to non-matter or spirit. Perhaps not in the one but in the zero the true divine nature.</p>
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		<title>
		By: Gary B Meisner		</title>
		<link>https://www.goldennumber.net/circles/#comment-6134</link>

		<dc:creator><![CDATA[Gary B Meisner]]></dc:creator>
		<pubDate>Sun, 25 Jul 2021 14:25:16 +0000</pubDate>
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					<description><![CDATA[In reply to &lt;a href=&quot;https://www.goldennumber.net/circles/#comment-6131&quot;&gt;Willie&lt;/a&gt;.

See https://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml.]]></description>
			<content:encoded><![CDATA[<p>In reply to <a href="https://www.goldennumber.net/circles/#comment-6131">Willie</a>.</p>
<p>See <a href="https://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml" rel="nofollow ugc">https://www.cut-the-knot.org/do_you_know/GoldenRatio.shtml</a>.</p>
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		<title>
		By: Willie		</title>
		<link>https://www.goldennumber.net/circles/#comment-6131</link>

		<dc:creator><![CDATA[Willie]]></dc:creator>
		<pubDate>Fri, 23 Jul 2021 13:59:22 +0000</pubDate>
		<guid isPermaLink="false">http://www.phisource.com/?p=386#comment-6131</guid>

					<description><![CDATA[How can the second one (Equilateral triangle construction) be proved?]]></description>
			<content:encoded><![CDATA[<p>How can the second one (Equilateral triangle construction) be proved?</p>
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		<title>
		By: Gary B Meisner		</title>
		<link>https://www.goldennumber.net/circles/#comment-5667</link>

		<dc:creator><![CDATA[Gary B Meisner]]></dc:creator>
		<pubDate>Fri, 22 Jan 2021 19:05:32 +0000</pubDate>
		<guid isPermaLink="false">http://www.phisource.com/?p=386#comment-5667</guid>

					<description><![CDATA[In reply to &lt;a href=&quot;https://www.goldennumber.net/circles/#comment-5657&quot;&gt;Dave Bell&lt;/a&gt;.

C is the center of the circle with a radius of length CD, also CE.

With D now known, D is the center of the circle with the same radius length DC, also DF.

You can&#039;t move C and D. They&#039;re the center and circumference of the same circle.]]></description>
			<content:encoded><![CDATA[<p>In reply to <a href="https://www.goldennumber.net/circles/#comment-5657">Dave Bell</a>.</p>
<p>C is the center of the circle with a radius of length CD, also CE.</p>
<p>With D now known, D is the center of the circle with the same radius length DC, also DF.</p>
<p>You can&#8217;t move C and D. They&#8217;re the center and circumference of the same circle.</p>
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		<title>
		By: Dave Bell		</title>
		<link>https://www.goldennumber.net/circles/#comment-5657</link>

		<dc:creator><![CDATA[Dave Bell]]></dc:creator>
		<pubDate>Tue, 12 Jan 2021 22:22:19 +0000</pubDate>
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					<description><![CDATA[Something seems (to me) to be missing from the &quot;Overlapping circles construction&quot;
What sets the spacing between points C and D?

My first construction attempt almost nailed Phi (a few PPM too large.)
Moving C and D  even a small amount  makes a big difference in the ratio AB/BG]]></description>
			<content:encoded><![CDATA[<p>Something seems (to me) to be missing from the &#8220;Overlapping circles construction&#8221;<br />
What sets the spacing between points C and D?</p>
<p>My first construction attempt almost nailed Phi (a few PPM too large.)<br />
Moving C and D  even a small amount  makes a big difference in the ratio AB/BG</p>
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		<item>
		<title>
		By: Gary B Meisner		</title>
		<link>https://www.goldennumber.net/circles/#comment-4043</link>

		<dc:creator><![CDATA[Gary B Meisner]]></dc:creator>
		<pubDate>Mon, 12 Feb 2018 10:46:39 +0000</pubDate>
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					<description><![CDATA[In reply to &lt;a href=&quot;https://www.goldennumber.net/circles/#comment-4039&quot;&gt;John Flinn&lt;/a&gt;.

With respect to the phi &quot;magic&quot; of the square and pentagon, see the constructions at https://www.goldennumber.net/geometry/. Not every polygon though up to one with an infinite number of sides relates to phi.]]></description>
			<content:encoded><![CDATA[<p>In reply to <a href="https://www.goldennumber.net/circles/#comment-4039">John Flinn</a>.</p>
<p>With respect to the phi &#8220;magic&#8221; of the square and pentagon, see the constructions at <a href="https://www.goldennumber.net/geometry/" rel="ugc">https://www.goldennumber.net/geometry/</a>. Not every polygon though up to one with an infinite number of sides relates to phi.</p>
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		<item>
		<title>
		By: John Flinn		</title>
		<link>https://www.goldennumber.net/circles/#comment-4039</link>

		<dc:creator><![CDATA[John Flinn]]></dc:creator>
		<pubDate>Sun, 11 Feb 2018 19:03:24 +0000</pubDate>
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					<description><![CDATA[Hi Gary,
    Thanks for your insight.  I think I find Phi even more interesting than Pi.  However I would like to extrapolate what happens when you inscribe other geometric figures inside the circle.  So far we have Pi = the ratio of the circumference of the circle to its diameter, Phi is the ratio of the circumference of the circle to the equilateral triangle etc. but what magic do we have with the circumference of the circle to the square, the pentagon, the hexagon ...the nagon? With the number of sides this ratio of course approaches 1.]]></description>
			<content:encoded><![CDATA[<p>Hi Gary,<br />
    Thanks for your insight.  I think I find Phi even more interesting than Pi.  However I would like to extrapolate what happens when you inscribe other geometric figures inside the circle.  So far we have Pi = the ratio of the circumference of the circle to its diameter, Phi is the ratio of the circumference of the circle to the equilateral triangle etc. but what magic do we have with the circumference of the circle to the square, the pentagon, the hexagon &#8230;the nagon? With the number of sides this ratio of course approaches 1.</p>
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		<item>
		<title>
		By: DarkLight		</title>
		<link>https://www.goldennumber.net/circles/#comment-3997</link>

		<dc:creator><![CDATA[DarkLight]]></dc:creator>
		<pubDate>Sat, 13 Jan 2018 09:59:27 +0000</pubDate>
		<guid isPermaLink="false">http://www.phisource.com/?p=386#comment-3997</guid>

					<description><![CDATA[Simply beautifull]]></description>
			<content:encoded><![CDATA[<p>Simply beautifull</p>
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