document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031251>Question 1031251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the figure below, the innermost circle has radius 1. \r<BR>\n" );
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document.write( "It is circumscribed by an equilateral triangle, which is circumscribed by a circle, which is circumscribed by a square, which is circumscribed by yet another circle, and so forth.\r<BR>\n" );
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document.write( "Answer two questions:\r<BR>\n" );
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document.write( "1. What is the radius of the outermost circle?<BR>\n" );
document.write( "2. Is finding the value of this radius an exercise/problem in discrete mathematics or continuous mathematics?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"https://i.imgsafe.org/ce48966.jpg\">\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646023 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a problem in discrete mathematics, consider the definition of a circle in discrete mathematics<BR>\n" );
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document.write( "the circle is comprised of polygons of n sides as n approaches infinity<BR>\n" );
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document.write( "begin with the circle of radius 1 inscribed in the equilateral triangle<BR>\n" );
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document.write( "the radius of the next circle is 1 / sin 30 = 2<BR>\n" );
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document.write( "the interior angle of regular polygon is (n-2)180/n<BR>\n" );
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document.write( "the hypotenuse (radius of the next circle) = radius of previous circle / the sin of (interior angle / 2)<BR>\n" );
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document.write( "the radius of the next circle is 2 / sin 45 = 2.828427125<BR>\n" );
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document.write( "the radius of the next circle is 2.828427125 / sin 54 = 3.496128196<BR>\n" );
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document.write( "the radius of the next circle is 3.496128196 / sin 60 = 4.03698111<BR>\n" );
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document.write( "the radius of the next circle is 4.03698111 / sin 64.28 = 4.480926229<BR>\n" );
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document.write( "the radius of the next circle is 4.480926229 / sin 67.5 = 4.8501196<BR>\n" );
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document.write( "the radius of the next circle is 4.8501196 / sin 70 = 5.161389472<BR>\n" );
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document.write( "now we look for the limit of this sequence<BR>\n" );
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document.write( "The limit of this sequence is \"Polygon Circumscribing Constant\" which is defined as<BR>\n" );
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document.write( "limit for n > = 3 of the product of 1 / cos(pi/n) = 8.7000366<BR>\n" );
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