#OK to post valentine 
#Natalya Ter-Saakov, Feb 13, Valentine 
with(plots):

r:=sqrt(x^2+y^2): t:= arctan(y/x): simplify(1-sin(t)=r);
                                           
s:= solve({1 - (y3/4)/(sqrt((x3^2 + (y3/4)^2)/x3^2)*x3) = sqrt(x3^2 + y3^2),x3=1.03});
assign(s);y3;

P1:=implicitplot(1 - (y/4)/(sqrt((x^2 + (y/4)^2)/x^2)*x) = sqrt(x^2 + y^2), x=0.0000000001..2, y=y3..1,color=red);
P2:=implicitplot(1 - (y/4)/(-sqrt((x^2 + (y/4)^2)/x^2)*x) = sqrt(x^2 + y^2), x=-2..-0.0000000001, y=y3..1,color=red); 
            
P3:=plot((tan(((3*Pi)/4 - arccot(3))*(x/1.03)-5*Pi/4)-3)/2+y3,x=0..1.03, color=red, view=[0..2, -3..0]);
P4:=plot((tan(((3*Pi)/4 - arccot(3))*(-x/1.03)-5*Pi/4)-3)/2+y3,x=-1.03..0, color=red, view=[-2..0, -3..0]);

P5:=textplot([[0, -0.3, "I love", 'font' = ["times", "roman", 24]],
 [0, -0.7, "perfect numbers", 'font' = ["times", "roman", 24]]],'color'="Crimson", 'view' = [-2 .. 2, -3 .. 2]);

#6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128,
P6:=textplot([[-0.85,0, "6", 'font' = ["times", "roman", 20], 'rotation' = 0],
 [-0.5, 0.15, "28", 'font' = ["times", "roman", 19],'rotation' = Pi/6],
 [-0.6, -0.3, "496", 'font' = ["times", "roman", 18],'rotation' = -Pi/12],
 [0.4,-1.1, "8128", 'font' = ["times", "roman", 17],'rotation' = -Pi/6],
 [-0.35, -1.1, "33550336", 'font' = ["times", "roman", 16],'rotation' = Pi/12],
 [0.5, -0.1, "8589869056", 'font' = ["times", "roman", 14],'rotation' = -Pi/10],
 [-0.1, -1.7, "137438691328", 'font' = ["times", "roman", 13],'rotation' = -Pi/20],
 [0, -1.4, "2305843008139952128", 'font' = ["times", "roman", 10],'rotation' = 0]],
 'color'="magenta", 'view' = [-2 .. 2, -3 .. 2]);

display([P1,P2, P3, P4, P5, P6], axes=None, 'view' = [-1.2 .. 1.2, -2.5 .. 1]);