Newton's cubic curve
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This article from The Guardian discusses Isaac Newton's investigation of the properties of the curve $x^3 – abx + a^3 – cy^2 = 0$, where $a, b$ and $c$ are constants. The image above is the curve of this equation when $a = 1, c = 4$ and $b$ ranges from –8 to 8.
The image seemsextremely aesthetic to me , almost artistic work. I'd have image on the wall like a poster, but with
ContourPlot[
Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 5, y, -5, 5,
Frame -> None, ImageSize -> 600, ContourStyle -> Black, PlotPoints -> 20]
I can not reproduce that image. The result is a bit different. Can someone please explain what is wrong with my code?
plotting
edited 1 hour ago
m_goldberg
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
5
down vote
favorite
This article from The Guardian discusses Isaac Newton's investigation of the properties of the curve $x^3 – abx + a^3 – cy^2 = 0$, where $a, b$ and $c$ are constants. The image above is the curve of this equation when $a = 1, c = 4$ and $b$ ranges from –8 to 8.
The image seemsextremely aesthetic to me , almost artistic work. I'd have image on the wall like a poster, but with
ContourPlot[
Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 5, y, -5, 5,
Frame -> None, ImageSize -> 600, ContourStyle -> Black, PlotPoints -> 20]
I can not reproduce that image. The result is a bit different. Can someone please explain what is wrong with my code?
plotting
edited 1 hour ago
m_goldberg
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range ofxto e.g.x, -5, 3.5.
– MarcoB
10 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago
add a comment |Â
up vote
5
down vote
favorite
up vote
5
down vote
favorite
This article from The Guardian discusses Isaac Newton's investigation of the properties of the curve $x^3 – abx + a^3 – cy^2 = 0$, where $a, b$ and $c$ are constants. The image above is the curve of this equation when $a = 1, c = 4$ and $b$ ranges from –8 to 8.
The image seemsextremely aesthetic to me , almost artistic work. I'd have image on the wall like a poster, but with
ContourPlot[
Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 5, y, -5, 5,
Frame -> None, ImageSize -> 600, ContourStyle -> Black, PlotPoints -> 20]
I can not reproduce that image. The result is a bit different. Can someone please explain what is wrong with my code?
plotting
edited 1 hour ago
m_goldberg
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
This article from The Guardian discusses Isaac Newton's investigation of the properties of the curve $x^3 – abx + a^3 – cy^2 = 0$, where $a, b$ and $c$ are constants. The image above is the curve of this equation when $a = 1, c = 4$ and $b$ ranges from –8 to 8.
The image seemsextremely aesthetic to me , almost artistic work. I'd have image on the wall like a poster, but with
ContourPlot[
Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 5, y, -5, 5,
Frame -> None, ImageSize -> 600, ContourStyle -> Black, PlotPoints -> 20]
I can not reproduce that image. The result is a bit different. Can someone please explain what is wrong with my code?
plotting
plotting
edited 1 hour ago
m_goldberg
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
m_goldberg
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
m_goldberg
82.6k870190
edited 1 hour ago
m_goldberg
82.6k870190
edited 1 hour ago
m_goldberg
82.6k870190
82.6k870190
asked 10 hours ago
Darko G
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
Darko G
261
asked 10 hours ago
Darko G
261
261
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range ofxto e.g.x, -5, 3.5.
– MarcoB
10 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago
add a comment |Â
2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range ofxto e.g.x, -5, 3.5.
– MarcoB
10 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago
2
2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is
x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.– MarcoB
10 hours ago
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is
x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.– MarcoB
10 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
7
down vote
You are plotting wrong equation, See this.
a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3.,
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600,
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]
I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.
It plots as: 
answered 10 hours ago
Sachin Kumar
1727
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
You are plotting wrong equation, See this.
a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3.,
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600,
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]
I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.
It plots as:
answered 10 hours ago
Sachin Kumar
1727
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
add a comment |Â
up vote
7
down vote
You are plotting wrong equation, See this.
a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3.,
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600,
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]
I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.
It plots as:
answered 10 hours ago
Sachin Kumar
1727
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
add a comment |Â
up vote
7
down vote
up vote
7
down vote
You are plotting wrong equation, See this.
a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3.,
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600,
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]
I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.
It plots as:
answered 10 hours ago
Sachin Kumar
1727
You are plotting wrong equation, See this.
a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3.,
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600,
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]
I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.
It plots as:
answered 10 hours ago
Sachin Kumar
1727
edited 8 hours ago
answered 10 hours ago
Sachin Kumar
1727
answered 10 hours ago
Sachin Kumar
1727
answered 10 hours ago
Sachin Kumar
1727
1727
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
add a comment |Â
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
1
1
You can maintain sharpness while increasing the number of steps (
b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]– Bob Hanlon
9 hours ago
You can maintain sharpness while increasing the number of steps (
b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]– Bob Hanlon
9 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago
add a comment |Â
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
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2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is
x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range ofxto e.g.x, -5, 3.5.– MarcoB
10 hours ago
I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
9 hours ago