User:Emerald block
Revision as of 22:52, 10 January 2020 by Emerald block (talk | contribs)
Hi! Welcome to my user page. There's not much here right now, but please enjoy this diagram of a ruler-and-compass construction of a regular pentagon.
![[asy] import geometry; unitsize(2cm); pair O,R,M; O = (0,0); dot(O); label("$O$",O,SW); R = (0,2); dot(R); label("$R$",R,NE); draw(circle(O,distance(O,R))); draw(O--R); draw(O-1.5(R-O)--O+1.5(R-O),dashed,Arrows); draw(rotate(90,O)*(O-1.5(R-O)--O+1.5(R-O)),red+dashed,Arrows); markscalefactor=.02; draw(rightanglemark(R,O,rotate(-90,O)*R),red); draw(O--rotate(-90,O)*R,invisible,StickIntervalMarker(2,1,red)); M = (O+rotate(-90,O)*R)/2; dot(M,red); draw(circle(M,distance(O,M)),green); draw(M+(M-rotate(180,O)*R)--rotate(180,O)*R+.5(rotate(180,O)*R-M),green+dashed,Arrows); draw(circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)-distance(O,M)),blue); draw(circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)+distance(O,M)),blue); draw(R --intersectionpoint(R..rotate(90,O)*R..rotate(180,O)*R,circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)+distance(O,M))) --intersectionpoint(R..rotate(90,O)*R..rotate(180,O)*R,circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)-distance(O,M))) --intersectionpoint(R..rotate(-90,O)*R..rotate(180,O)*R,circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)-distance(O,M))) --intersectionpoint(R..rotate(-90,O)*R..rotate(180,O)*R,circle(rotate(180,O)*R,distance(M,rotate(180,O)*R)+distance(O,M))) --cycle,linewidth(1.5)); [/asy]](http://latex.artofproblemsolving.com/5/9/d/59d557ef6cb8a442892a29fd37a4b8823c7f5a9c.png)
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