%mainfile=fractions
verbatimtex 			%uses LaTex
\documentclass{article} 
\usepackage{euler}              %typesets the math text using the font Euler
\begin{document} 
etex;

beginfig(1); 	%file=general-frac.eps
  z0=(0,0);	%defines the first point at coordinates (0,0)
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;		%defines the point z3 to be (-1in,0)
  z4=-z2;
    
  draw z1..z2..z3..z4..cycle;	%draws a curve thru points z1,z2,z3,z4 and cycles back to z1
  draw z0--z1;			%draws a straight line from z0 to z1
  draw z0--1in*dir 20;		%draws a line starting from z0 to 20 degrees above the horiz
                                % 1 inch in length from the ref from the orgin
  draw z0--1in*dir 40;		%sameas above except 40 degrees above the horiz
  draw z0--1in*dir 60;
  draw z0--1in*dir 80;
  
  draw z0--1in*dir 140;
  draw z0--1in*dir 160;
  draw z0--1in*dir 180;
  
  draw z0--1in*dir -20;
  
  label(btex $1$ etex, .7in*dir 10);	%typesets the label 1 and puts it .7 inches from
                                        % the origin 10 degrees above horiz
  label(btex $2$ etex, .7in*dir 30);
  label(btex $3$ etex, .7in*dir 50);
  label(btex $a$ etex, .7in*dir 150);
  label(btex $a+1$ etex, .7in*dir 170);
  label(btex $b$ etex, .7in*dir -10);
  
  pickup pencircle scaled 4pt; 			%changes thinkness of the pen to make the
                                                % ellipses points bigger
  
  draw .7in*dir 90;				%draws the ellipses
  draw .7in*dir 110;
  draw .7in*dir 130;
  
  draw .7in*dir 220;
  draw .7in*dir 260;
  draw .7in*dir 300;
    
endfig;					%end of figure

beginfig(2);%file=one-over-b.eps
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  draw z0--z1..z2..1in*dir 160--cycle;
  draw z0--1in*dir 20;
  draw z0--1in*dir 40;
  draw z0--1in*dir 60;
  draw z0--1in*dir 80;
  
  draw z0--1in*dir 140;
  draw z0--1in*dir 160;
  
  label(btex $1$ etex, .7in*dir 10);
  label(btex $2$ etex, .7in*dir 30);
  label(btex $3$ etex, .7in*dir 50);
  label(btex $a$ etex, .7in*dir 150);
  
  pickup pencircle scaled 4pt;

  draw .7in*dir 90;
  draw .7in*dir 110;
  draw .7in*dir 130;

  pickup pencircle scaled 0pt;

  draw 1in*dir 270;

endfig;

beginfig(3);%file=two-fifths.eps
  
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;							%name of path
  p:=z0--1in*dir 0..1in*dir 72..1in*dir 144--cycle;	%outlines the path
  fill p withcolor .8*white;				%fills the path with a light gray
  
  draw z1..z2..z3..z4..cycle;				%note the circle is drawn after the filled path, o.w. the path draws over the circle
  draw z0--1in*dir 0;
  draw z0--1in*dir 72;
  draw z0--1in*dir 144;
  draw z0--1in*dir 216;
  draw z0--1in*dir 288;
  
  
endfig;

beginfig(4);%file=seven-thirds.eps
  
  z0=(0,0); z1=(1in,0); z2=(0,1in); z3=-z1; z4=-z2;
  z10=(3in,0); z11=(4in,0); z12=(3in,1in); z13=(2in,0); z14=(3in,-1in);
  z20=(5.5in,0);

  path p,q,r;		
  p:=1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 270..cycle;
  q:=z10+1in*dir 0..z10+1in*dir 90..z10+1in*dir 180..z10+1in*dir 270..cycle;
  r:=z20--z20+1in*dir 0..z20+1in*dir 60..z20+1in*dir 120--cycle;
  fill p withcolor .8*white;
  fill q withcolor .8*white;
  fill r withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;
  
  draw z11..z12..z13..z14..cycle;
  draw z10--z11;%1in*dir 0;
  draw z10--z10+1in*dir 120;
  draw z10--z10+1in*dir 240;
  
  draw z20--z20+1in*dir 0..z20+1in*dir 60..z20+1in*dir 120--cycle;
  
endfig;



beginfig(5);%file=four-sixths.eps
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 240--cycle;
  fill p withcolor .8*white;

  draw z1..z2..z3..z4..cycle;
    
  draw z0--1in*dir 0;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;
  draw z0--1in*dir 180;
  draw z0--1in*dir 240;
  draw z0--1in*dir 300;
    
endfig;

beginfig(6);%file=seven-tenths.eps
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 252--cycle;
  fill p withcolor .8*white;

  draw z1..z2..z3..z4..cycle;
    
  draw z0--1in*dir 0;
  draw z0--1in*dir 36;
  draw z0--1in*dir 72;
  draw z0--1in*dir 108;
  draw z0--1in*dir 144;
  draw z0--1in*dir 180;
  draw z0--1in*dir 216;
  draw z0--1in*dir 252;
  draw z0--1in*dir 288;
  draw z0--1in*dir 324;
    
endfig;

beginfig(7);%file=four-fourths.eps
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 270..cycle;
  fill p withcolor .8*white;

  draw z1..z2..z3..z4..cycle;
    
  draw z0--1in*dir 0;
  draw z0--1in*dir 90;
  draw z0--1in*dir 180;
  draw z0--1in*dir 270;
    
endfig;

beginfig(8);%file=zero-fifths.eps
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  draw z1..z2..z3..z4..cycle;
    
  draw z0--1in*dir 0;
  draw z0--1in*dir 72;
  draw z0--1in*dir 144;
  draw z0--1in*dir 216;
  draw z0--1in*dir 288;
      
endfig;

beginfig(9);%file=three-halves.eps
  
  pair s,t,u;
  s:=(0,.125in);
  t:=(2.5in,0);
  u:=(5in,0);

  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;

  path l,m,n,o,p,q;
  l:=z1+s..z2+s..z3+s--cycle;
  m:=-z1-s..-z2-s..-z3-s--cycle;
  n:=z1+s+t..z2+s+t..z3+s+t--cycle;
  o:=-z1-s+t..-z2-s+t..-z3-s+t--cycle;
  p:=z1+s+u..z2+s+u..z3+s+u--cycle;
  q:=-z1-s+u..-z2-s+u..-z3-s+u--cycle;
  fill l withcolor .8*white;
  fill m withcolor .8*white;
  fill n withcolor .8*white;
  fill o withcolor .8*white;
  fill p withcolor .8*white;
  fill q withcolor .8*white;
  
  draw z1+s..z2+s..z3+s--cycle;
  draw -z1-s..-z2-s..-z3-s--cycle;
  
  draw z1+s+t..z2+s+t..z3+s+t--cycle;
  draw -z1-s+t..-z2-s+t..-z3-s+t--cycle;
  
  draw z1+s+u..z2+s+u..z3+s+u--cycle;
  draw -z1-s+u..-z2-s+u..-z3-s+u--cycle;
  
endfig;

beginfig(10);%file=zero-thirds.eps
  
  z0=(0,0);
  
  draw 1in*dir 0..1in*dir 120..1in*dir 240..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;
  
endfig;

beginfig(11);%file=half-one-third.eps
  
  z0=(0,0);
  
  pair s[],a[];
  a[1]:=(1.2in,0);
  a[2]:=(1.8in,0);
  a[3]:=(3.7in,0);
  a[4]:=(4.3in,0);
  a[5]:=(6.2in,0);
  a[6]:=(6.8in,0);
  s[1]:=(2.5in,0);
  s[2]:=(5in,0);
  s[3]:=(7in,0);

  draw z0--1in*dir 120..1in*dir 240..1in*dir 0--cycle;
  draw z0--1in*dir 240;
  
  drawarrow a[1]..a[2];
  
  draw z0+s[1]--1in*dir 0+s[1]..1in*dir 60+s[1]..1in*dir 120+s[1]--cycle;
  
  drawarrow a[3]..a[4];
  
  draw z0+s[2]--1in*dir 0+s[2]..1in*dir 60+s[2]..1in*dir 120+s[2]--cycle;
  draw z0+s[2]--1in*dir 60+s[2];
  
  drawarrow a[5]..a[6];
  
  draw z0+s[3]--1in*dir 0+s[3]..1in*dir 30+s[3]..1in*dir 60+s[3]--cycle;
  
endfig;

beginfig(12);%file=one-sixth.eps

  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 30..1in*dir 60--cycle;
  fill p withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;
  draw z0--1in*dir 180;
  draw z0--1in*dir 240;
  draw z0--1in*dir 300;
  draw z0--1in*dir 360;
  
endfig;

beginfig(13);%file=third-one-half.eps

  z0=(0,0);

  pair s[],a[];
  a[1]:=(1.2in,0);
  a[2]:=(1.8in,0);
  a[3]:=(4.2in,0);
  a[4]:=(4.8in,0);
  a[5]:=(7.2in,0);
  a[6]:=(7.8in,0);
  s[1]:=(3in,0);
  s[2]:=(6in,0);
  s[3]:=(8in,0);
  
  draw 1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 270..cycle;
  draw 1in*dir 0--1in*dir 180;
  
  drawarrow a[1]..a[2];
  
  draw 1in*dir 0+s[1]..1in*dir 90+s[1]..1in*dir 180+s[1]--cycle;
  
  drawarrow a[3]..a[4];
  
  draw 1in*dir 0+s[2]..1in*dir 90+s[2]..1in*dir 180+s[2]--cycle;
  draw z0+s[2]--1in*dir 60+s[2];
  draw z0+s[2]--1in*dir 120+s[2];
  
  drawarrow a[5]..a[6];
  
  draw z0+s[3]--1in*dir 0+s[3]..1in*dir 30+s[3]..1in*dir 60+s[3]--cycle;
  
endfig;

beginfig(14);%file=two-sixths.eps
  
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 60..1in*dir 120--cycle;
  fill p withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;
  draw z0--1in*dir 180;
  draw z0--1in*dir 240;
  draw z0--1in*dir 300;
  draw z0--1in*dir 360;
  
endfig;

beginfig(15);%file=three-divided-half.eps
  
  pair t,u;
  t:=(2.5in,0);
  u:=(5in,0);
  
  z1=(1in,0);
  z2=(0,1in);
  z3=(-1in,0);
  z4=(0,-1in);

  path p,q,r;
  p:=z1..z2..z3..z4..cycle;
  q:=z1+t..z2+t..z3+t..z4+t..cycle;
  r:=z1+u..z2+u..z3+u..z4+u..cycle;
  fill p withcolor .8*white;
  fill q withcolor .8*white;
  fill r withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z1--z3;
  
  draw z1+t..z2+t..z3+t..z4+t..cycle;
  draw z1+t--z3+t;
  
  draw z1+u..z2+u..z3+u..z4+u..cycle;
  draw z1+u--z3+u;

endfig;

beginfig(16);%file=twofifths-plus-onefifth.eps

  pair s,t;
  s:=(2.5in,0);
  t:=(5in,0);
  
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  z5=s+z0;
  z6=s+z1;
  z7=s+z2;
  z8=s+z3;
  z9=s+z4;

  z10=t+z0;
  z11=t+z1;
  z12=t+z2;
  z13=t+z3;
  z14=t+z4;
  
  path p,q,r;
  p:=z0--1in*dir 0..1in*dir 72..1in*dir 144--cycle;
  fill p withcolor .8*white;
  q:=z5--s+1in*dir 0..s+1in*dir 36..s+1in*dir 72--cycle;
  fill q withcolor .8*white;
  r:=z10--t+1in*dir 0..t+1in*dir 72..t+1in*dir 144..t+1in*dir 216--cycle;
  fill r withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 72;
  draw z0--1in*dir 144;
  draw z0--1in*dir 216;
  draw z0--1in*dir 288;
  
  draw z6..z7..z8..z9..cycle;
  draw z5--s+1in*dir 0;
  draw z5--s+1in*dir 72;
  draw z5--s+1in*dir 144;
  draw z5--s+1in*dir 216;
  draw z5--s+1in*dir 288;

  draw z11..z12..z13..z14..cycle;
  draw z10--t+1in*dir 0;
  draw z10--t+1in*dir 72;
  draw z10--t+1in*dir 144;
  draw z10--t+1in*dir 216;
  draw z10--t+1in*dir 288;
  
  pickup pencircle scaled 2pt;
  
%label(btex $+$ etex, (1.25in,0));
  draw (1.25in,.15in)--(1.25in,-.15in);
  draw (1.1in,0)--(1.4in,0);
  
%label(btex $=$ etex, (3.75in,0));
  draw (3.65in,.05in)--(3.85in,.05in);
  draw (3.65in,-.05in)--(3.85in,-.05in);

endfig;

beginfig(17);%file=half-third.eps
  
  pair s;
  s:=(3in,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p[];
  p[1]:=z0--1in*dir 0..1in*dir 90..1in*dir 180--cycle;
  p[2]:=z0+s--1in*dir -120+s..1in*dir -60+s..1in*dir 0+s--cycle;
  fill p[1] withcolor .8*white;
  fill p[2] withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw 1in*dir 0--1in*dir 180;
  
  draw z1+s..z2+s..z3+s..z4+s..cycle;
  draw z0+s--1in*dir 0+s;
  draw z0+s--1in*dir 120+s;
  draw z0+s--1in*dir 240+s;

endfig;

beginfig(18);%file=halfthird-pacman.eps

  
  z0=(0,0);
  
  path p;
  p:=z0--1in*dir -120..1in*dir 0..1in*dir 90..1in*dir 180--cycle;
  fill p withcolor .8*white;
  
  draw z0--1in*dir -120..1in*dir 0..1in*dir 90..1in*dir 180--cycle;
  
endfig;

beginfig(19);%file=half-third-sixths.eps
  
  pair s;
  s:=(3in,0);
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p,q;
  p:=z0--1in*dir 0..1in*dir 60..1in*dir 120..1in*dir 180--cycle;
  fill p withcolor .8*white;
  q:=s+z0--s+1in*dir -120..s+1in*dir -60..s+1in*dir 0--cycle;
  fill q withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;
  draw z0--1in*dir 180;
  draw z0--1in*dir 240;
  draw z0--1in*dir 300;
  draw z0--1in*dir 360;
  
  draw s+z1..s+z2..s+z3..s+z4..cycle;
  draw s+z0--s+1in*dir 0;
  draw s+z0--s+1in*dir 60;
  draw s+z0--s+1in*dir 120;
  draw s+z0--s+1in*dir 180;
  draw s+z0--s+1in*dir 240;
  draw s+z0--s+1in*dir 300;
  draw s+z0--s+1in*dir 360;
  
endfig;

beginfig(20);%file=half-third-sum.eps

  z0=(0,0);

  path p;
  p:=z0--1in*dir -120..1in*dir 0..1in*dir 90..1in*dir 180--cycle;
  fill p withcolor .8*white;
  
  draw z0--1in*dir 180..1in*dir 90..1in*dir 0..1in*dir -90..1in*dir -120--cycle;
  draw z0--1in*dir -60;
  draw z0--1in*dir 0;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;

endfig;

beginfig(21);%file=fivesixths-threefourths-sum.eps

  pickup pencircle scaled 2.1bp;
  
  pair s[],t[];
  z0=(0,0);
  s[1]:=(3in,0);
  s[2]:=(6in,0);
  s[3]:=(9in,0);
  t[1]:=(0,-3in);
  
  draw z0--1in*dir 0..1in*dir 90..1in*dir 180..1in*dir 270..1in*dir 300--cycle;
  draw z0--1in*dir 60;
  draw z0--1in*dir 120;
  draw z0--1in*dir 180;
  draw z0--1in*dir 240;
  


  draw z0+s[1]--1in*dir 0+s[1]..1in*dir 90+s[1]..1in*dir 180+s[1]..1in*dir 270+s[1]--cycle;
  draw z0+s[1]--1in*dir 90+s[1];
  draw z0+s[1]--1in*dir 180+s[1];
  
  draw z0+t[1]--1in*dir 0+t[1]..1in*dir 90+t[1]..1in*dir 180+t[1]..1in*dir 270+t[1]..1in*dir 300+t[1]--cycle;
  draw z0+t[1]--1in*dir 30+t[1];
  draw z0+t[1]--1in*dir 60+t[1];
  draw z0+t[1]--1in*dir 90+t[1];
  draw z0+t[1]--1in*dir 120+t[1];
  draw z0+t[1]--1in*dir 150+t[1];
  draw z0+t[1]--1in*dir 180+t[1];
  draw z0+t[1]--1in*dir 210+t[1];
  draw z0+t[1]--1in*dir 240+t[1];
  draw z0+t[1]--1in*dir 270+t[1];



  draw z0+s[1]+t[1]--1in*dir 0+s[1]+t[1]..1in*dir 90+s[1]+t[1]..1in*dir 180+s[1]+t[1]..1in*dir 270+s[1]+t[1]--cycle;
  draw z0+s[1]+t[1]--1in*dir 30+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 60+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 90+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 120+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 150+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 180+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 210+s[1]+t[1];
  draw z0+s[1]+t[1]--1in*dir 240+s[1]+t[1];
  


  draw 1in*dir 0+s[2]+t[1]..1in*dir 90+s[2]+t[1]..1in*dir 180+s[2]+t[1]..1in*dir 270+s[2]+t[1]..cycle;
  draw z0+s[2]+t[1]--1in*dir 0+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 30+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 60+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 90+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 120+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 150+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 180+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 210+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 240+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 270+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 300+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 330+s[2]+t[1];
  draw z0+s[2]+t[1]--1in*dir 360+s[2]+t[1];
  
  draw z0+s[3]+t[1]--1in*dir 0+s[3]+t[1]..1in*dir 90+s[3]+t[1]..1in*dir 180+s[3]+t[1]..1in*dir 210+s[3]+t[1]--cycle;
  draw z0+s[3]+t[1]--1in*dir 30+s[3]+t[1];
  draw z0+s[3]+t[1]--1in*dir 60+s[3]+t[1];
  draw z0+s[3]+t[1]--1in*dir 90+s[3]+t[1];
  draw z0+s[3]+t[1]--1in*dir 120+s[3]+t[1];
  draw z0+s[3]+t[1]--1in*dir 150+s[3]+t[1];
  draw z0+s[3]+t[1]--1in*dir 180+s[3]+t[1];
  
  pickup pencircle scaled 3pt;
  
%label(btex $+$ etex, (1.5in,0));
  draw (1.5in,.1in)--(1.5in,-.1in);
  draw (1.4in,0)--(1.6in,0);
  
%label(btex $+$ etex, (1.5in,0)+t[1]);
  draw (1.5in,.1in)+t[1]--(1.5in,-.1in)+t[1];
  draw (1.4in,0)+t[1]--(1.6in,0)+t[1];
  
  draw (4.4in,.05in)--(4.6in,.05in);
  draw (4.4in,-.05in)--(4.6in,-.05in);
  
%label(btex $=$ etex, (4.5in,0)+t[1]);
  draw (4.4in,.05in)+t[1]--(4.6in,.05in)+t[1];
  draw (4.4in,-.05in)+t[1]--(4.6in,-.05in)+t[1];

endfig;

beginfig(22);%file=two-thirds.eps

  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 120..1in*dir 240--cycle;
  fill p withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;
  
endfig;

beginfig(23);%file=thirds-divided-five.eps


  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 24;
  draw z0--1in*dir 48;
  draw z0--1in*dir 72;
  draw z0--1in*dir 96;
  draw z0--1in*dir 144;
  draw z0--1in*dir 168;
  draw z0--1in*dir 192;
  draw z0--1in*dir 216;
  draw z0--1in*dir 264;
  draw z0--1in*dir 288;
  draw z0--1in*dir 312;
  draw z0--1in*dir 336;
  
  pickup pencircle scaled 2pt;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;


endfig;

beginfig(24);%file=two-fifteenths.eps


  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 24..1in*dir 48--cycle;
  fill p withcolor .8*white;
  
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 24;
  draw z0--1in*dir 48;
  draw z0--1in*dir 72;
  draw z0--1in*dir 96;
  draw z0--1in*dir 144;
  draw z0--1in*dir 168;
  draw z0--1in*dir 192;
  draw z0--1in*dir 216;
  draw z0--1in*dir 264;
  draw z0--1in*dir 288;
  draw z0--1in*dir 312;
  draw z0--1in*dir 336;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;
  


endfig;

beginfig(25);%file=half-to-halfhalf.eps

  pair s;
  s:=(3in,0);
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  draw z1..z2..z3--cycle;
  
  drawarrow (1.2in,0)..(1.8in,0);
  
  draw s+z1..s+z2..s+z3--cycle;
  draw s+z0--s+1in*dir 90;
  
  
endfig;

beginfig(26);%file=half-dividedby-third.eps
  
  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;
  
  path p;
  p:=z0--1in*dir 0..1in*dir 90..1in*dir 180--cycle;
  fill p withcolor .8*white;
  
  pickup pencircle scaled 1pt;
  draw z1..z2..z3..z4..cycle;
  draw z1--z3;
  draw z0..1in*dir 120 dashed evenly;
  draw z0--1in*dir 240 dashed evenly;
  
endfig;

beginfig(27); %file=third-divby-half.eps

  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;

  path p;
  p:=z0--1in*dir 0..1in*dir 60..1in*dir 120--cycle;
  fill p withcolor .8*white;

  pickup pencircle scaled 1pt;
  draw z1..z2..z3..z4..cycle;
  draw z0--1in*dir 0;
  draw z0--1in*dir 120;
  draw z0--1in*dir 240;
  draw z0..1in*dir 180 dashed evenly;
  draw z0--1in*dir 60 dashed dashpattern(on 1bp off 3bp on 8bp off 3bp);;
endfig;

beginfig(28); %file=twofifths-divby-third.eps

  z0=(0,0);
  z0=(0,0);
  z1=(1in,0);
  z2=(0,1in);
  z3=-z1;
  z4=-z2;

  path p;
  p:=z0--1in*dir 0..1in*dir 72..1in*dir 144--cycle;
  fill p withcolor .8*white;

  pickup pencircle scaled 1pt;
  draw z1..z2..z3..z4..cycle;
  draw z0--z1;
  draw z0--1in*dir 72;
  draw z0--1in*dir 144;
  draw z0--1in*dir 216;
  draw z0--1in*dir 288;
  draw z0--1in*dir 120 dashed evenly;
  draw z0--1in*dir 240 dashed evenly;
endfig;

























\verbatimtex
\end{document}
etex;

end		%tells metapost this is the end of the file