Contour lines or Contour curve?
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For the plane $z=50$ on the surface $z=75-x^2-y^2$, the contour lines is the circle $x^2+y^2=25$ in the xy-plane.
My question is why we say "contour lines" not "contour curve", also we use "lines" not "line" ?
multivariable-calculus
edited Aug 25 at 11:43
user144410
7441519
asked Aug 25 at 11:28
Adesh Sharma
22
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For the plane $z=50$ on the surface $z=75-x^2-y^2$, the contour lines is the circle $x^2+y^2=25$ in the xy-plane.
My question is why we say "contour lines" not "contour curve", also we use "lines" not "line" ?
multivariable-calculus
edited Aug 25 at 11:43
user144410
7441519
asked Aug 25 at 11:28
Adesh Sharma
22
These terms are used interchangeably
– MPW
Aug 25 at 11:30
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13
add a comment |Â
up vote
0
down vote
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up vote
0
down vote
favorite
For the plane $z=50$ on the surface $z=75-x^2-y^2$, the contour lines is the circle $x^2+y^2=25$ in the xy-plane.
My question is why we say "contour lines" not "contour curve", also we use "lines" not "line" ?
multivariable-calculus
edited Aug 25 at 11:43
user144410
7441519
asked Aug 25 at 11:28
Adesh Sharma
22
For the plane $z=50$ on the surface $z=75-x^2-y^2$, the contour lines is the circle $x^2+y^2=25$ in the xy-plane.
My question is why we say "contour lines" not "contour curve", also we use "lines" not "line" ?
multivariable-calculus
edited Aug 25 at 11:43
user144410
7441519
asked Aug 25 at 11:28
Adesh Sharma
22
edited Aug 25 at 11:43
user144410
7441519
edited Aug 25 at 11:43
user144410
7441519
edited Aug 25 at 11:43
user144410
7441519
7441519
asked Aug 25 at 11:28
Adesh Sharma
22
asked Aug 25 at 11:28
Adesh Sharma
22
asked Aug 25 at 11:28
Adesh Sharma
22
22
These terms are used interchangeably
– MPW
Aug 25 at 11:30
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13
add a comment |Â
These terms are used interchangeably
– MPW
Aug 25 at 11:30
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13
These terms are used interchangeably
– MPW
Aug 25 at 11:30
These terms are used interchangeably
– MPW
Aug 25 at 11:30
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13
add a comment |Â
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These terms are used interchangeably
– MPW
Aug 25 at 11:30
if the graph of $z$ is chopped with the plane $z=50$, the resulting circle $x^2+y^2=25$ is the contour curve. It is a single curve and not a (straight) line. If the objective function $z$ is a linear function (of degree one), then there will be contour line (if cut by one plane) or contour lines (if cut by several planes).
– farruhota
Aug 25 at 12:13