(*^
::[	Information =

	"This is a Mathematica Notebook file.  It contains ASCII text, and can be
	transferred by email, ftp, or other text-file transfer utility.  It should
	be read or edited using a copy of Mathematica or MathReader.  If you 
	received this as email, use your mail application or copy/paste to save 
	everything from the line containing (*^ down to the line containing ^*)
	into a plain text file.  On some systems you may have to give the file a 
	name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
	The line below identifies what version of Mathematica created this file,
	but it can be opened using any other version as well.";

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	MacintoshStandardFontEncoding; 
	
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	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; 
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; 
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; 
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; 
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; 
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; 
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; 
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	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; 
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	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; 
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:[font = input; preserveAspect; startGroup]
Solve[{Cos[3Pi/5] - 1, Sin[3Pi/5],x}.{Cos[3Pi/5] - 1, Sin[3Pi/5],x}==
4 Cos[3Pi/5]^2, x]
:[font = output; output; inactive; preserveAspect; endGroup]
{{x -> -(-1 + 2*Cos[(3*Pi)/5] + 3*Cos[(3*Pi)/5]^2 - Sin[(3*Pi)/5]^2)^(1/2)}, 
 
  {x -> (-1 + 2*Cos[(3*Pi)/5] + 3*Cos[(3*Pi)/5]^2 - Sin[(3*Pi)/5]^2)^(1/2)}}
;[o]
                        3 Pi          3 Pi 2       3 Pi 2
{{x -> -Sqrt[-1 + 2 Cos[----] + 3 Cos[----]  - Sin[----] ]}, 
                         5             5            5
 
                        3 Pi          3 Pi 2       3 Pi 2
  {x -> Sqrt[-1 + 2 Cos[----] + 3 Cos[----]  - Sin[----] ]}}
                         5             5            5
:[font = input; preserveAspect; startGroup]
N[%]
:[font = output; output; inactive; preserveAspect; endGroup]
{{x -> 0. - 1.49534878122122*I}, {x -> 0. + 1.49534878122122*I}}
;[o]
{{x -> 0. - 1.49535 I}, {x -> 0. + 1.49535 I}}
:[font = input; preserveAspect; startGroup]
Do[Do[If[n/3<d, Print["{n,d} = ", {n,d}],],{d,n/2 - 1/2}];Print[" "],{n,5,30}]
:[font = print; inactive; preserveAspect; endGroup]
{n,d} = {5, 2}
 
 
{n,d} = {7, 3}
 
{n,d} = {8, 3}
 
{n,d} = {9, 4}
 
{n,d} = {10, 4}
 
{n,d} = {11, 4}
{n,d} = {11, 5}
 
{n,d} = {12, 5}
 
{n,d} = {13, 5}
{n,d} = {13, 6}
 
{n,d} = {14, 5}
{n,d} = {14, 6}
 
{n,d} = {15, 6}
{n,d} = {15, 7}
 
{n,d} = {16, 6}
{n,d} = {16, 7}
 
{n,d} = {17, 6}
{n,d} = {17, 7}
{n,d} = {17, 8}
 
{n,d} = {18, 7}
{n,d} = {18, 8}
 
{n,d} = {19, 7}
{n,d} = {19, 8}
{n,d} = {19, 9}
 
{n,d} = {20, 7}
{n,d} = {20, 8}
{n,d} = {20, 9}
 
{n,d} = {21, 8}
{n,d} = {21, 9}
{n,d} = {21, 10}
 
{n,d} = {22, 8}
{n,d} = {22, 9}
{n,d} = {22, 10}
 
{n,d} = {23, 8}
{n,d} = {23, 9}
{n,d} = {23, 10}
{n,d} = {23, 11}
 
{n,d} = {24, 9}
{n,d} = {24, 10}
{n,d} = {24, 11}
 
{n,d} = {25, 9}
{n,d} = {25, 10}
{n,d} = {25, 11}
{n,d} = {25, 12}
 
{n,d} = {26, 9}
{n,d} = {26, 10}
{n,d} = {26, 11}
{n,d} = {26, 12}
 
{n,d} = {27, 10}
{n,d} = {27, 11}
{n,d} = {27, 12}
{n,d} = {27, 13}
 
{n,d} = {28, 10}
{n,d} = {28, 11}
{n,d} = {28, 12}
{n,d} = {28, 13}
 
{n,d} = {29, 10}
{n,d} = {29, 11}
{n,d} = {29, 12}
{n,d} = {29, 13}
{n,d} = {29, 14}
 
{n,d} = {30, 11}
{n,d} = {30, 12}
{n,d} = {30, 13}
{n,d} = {30, 14}
 
^*)
