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J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
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My 3D plot of a Klein bottle doesn't look right

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

I am trying to plot it using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
  Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle.

enter image description here

The reference I am using is this onethis one (page 141) where you can see the same parameterization.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?

My 3D plot a Klein bottle doesn't look right

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

I am trying to plot it using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
  Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle.

enter image description here

The reference I am using is this one (page 141) where you can see the same parameterization.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?

My 3D plot of a Klein bottle doesn't look right

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

I am trying to plot it using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
  Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle.

enter image description here

The reference I am using is this one (page 141) where you can see the same parameterization.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?
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m_goldberg
m_goldberg
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My 3D plottingplot a Klein bottle won't work despite using correct parametrisationdoesn't look right

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

and then I am trying to plot it using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
  Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle: .

enter image description here

The reference I am using is this one (page 141) where you can see the same parametrisationparameterization.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?

3D plotting a Klein bottle won't work despite using correct parametrisation

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

and then I am trying to plot using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
 Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle: enter image description here

The reference I am using is this one (page 141) where you can see the same parametrisation.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?

My 3D plot a Klein bottle doesn't look right

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

I am trying to plot it using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
  Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle.

enter image description here

The reference I am using is this one (page 141) where you can see the same parameterization.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?
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Marion
Marion
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3D plotting a Klein bottle won't work despite using correct parametrisation

I have found the following parametrisation for a Klein bottle:

a = 6 Cos[2 u] (1 + Sin[u]);
b = 16 Sin[u];
c = 4 (1 - Cos[u]/2);
fx = If[Pi < u <= 0, a + c Cos[v + Pi], a + c Cos[u] Cos[v]];
fy = If[Pi < u < 2 Pi, b, b + c Sin[u] ];
fz = c Sin[v];

and then I am trying to plot using

ParametricPlot3D[{fx, fy, fz}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
 Boxed -> False, Axes -> False]

but the result is not quite the Klein bottle: enter image description here

The reference I am using is this one (page 141) where you can see the same parametrisation.

  1. Any ideas why it does not work with me?
  2. Also how can I change the colours of the surface to be as in the book?