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Question: boys surface - is it one surface

Question:boys surface - is it one surface

Christopher2222 5785 Maple
surface boys
November 21 2012
0

Maybe I'm missing something but I thought boys surface was one surface and when I plot it in maple it appears to have two surfaces.


restart; gc()

x := (sqrt(2)*cos(v)^2*cos(2*u)+cos(u)*sin(2*v))/(2-sqrt(2)*sin(3*u)*sin(2*v))

(2^(1/2)*cos(v)^2*cos(2*u)+cos(u)*sin(2*v))/(2-2^(1/2)*sin(3*u)*sin(2*v))

 (1)

y := (sqrt(2)*cos(v)^2*sin(2*u)-sin(u)*sin(2*v))/(2-sqrt(2)*sin(3*u)*sin(2*v))

(2^(1/2)*cos(v)^2*sin(2*u)-sin(u)*sin(2*v))/(2-2^(1/2)*sin(3*u)*sin(2*v))

 (2)

z := 3*cos(v)^2/(2-sqrt(2)*sin(3*u)*sin(2*v))

3*cos(v)^2/(2-2^(1/2)*sin(3*u)*sin(2*v))

 (3)

plot3d([x, y, z], u = -(1/2)*Pi .. (1/2)*Pi, v = 0 .. Pi, numpoints = 5000, axes = box)

  

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Download boys_surface2.mw

 
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