Explore Contour Lines in Geogebra: Drawing and Finding Functions

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In summary, the conversation was about finding contour lines in Geogebra for various functions. The appropriate commands and equations were discussed, including using the "Sequence" and "Intersect" functions. The conversation also included some troubleshooting and clarifying questions. In the end, the desired contour lines were successfully plotted for both functions.
  • #1
mathmari
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Hey! :eek:

I am looking at the following:

1. We have the function $f(x,y)=y-x^2-1$. Write the appropriate commands in Geogebra that draw a contour line with $f(x,y)=\frac{3709}{2000}$.

Could you give me a hint what command we have to use here? Do we just plot $y-x^2-1=\frac{1374}{2000}$ ? (Wondering)
2. Give the graph of the below functions in Geogebra and find the countour lines $f(x,y)=c$ where $c$ is in the interval $[0,10]$ and each contour line has to have distance from the next one $0.4$.
  • $f(x,y)=\cos (xy)$
  • $f(x,y)=\frac{2}{\sqrt{x^2+y^2}}+\frac{2}{\sqrt{(x-1)^2+y^2}}$

Do we use for that the command "Sequence(\cos (xy)=c, c, 0, 10)" ? (Wondering)
 
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  • #2
mathmari said:
Hey! :eek:

I am looking at the following:

1. We have the function $f(x,y)=y-x^2-1$. Write the appropriate commands in Geogebra that draw a contour line with $f(x,y)=\frac{3709}{2000}$.

Could you give me a hint what command we have to use here? Do we just plot $y-x^2-1=\frac{1374}{2000}$ ?

Hey mathmari!

A contour line is a curve on a surface $z=f(x,y)$ for a fixed $z$ isn't it? (Wondering)

But if we specify $y-x^2-1=\frac{1374}{2000}$, we do not get such a curve do we?
Instead we are getting a different surface.
Makes sense, because we have effectively specified an equation in x and y without specifying z.
So Geogebra shows a surface that satisfies the equation for x and y, and shows it for any z.
It's a parabolic cylinder. (Worried)

I think that instead we need the intersection of the surface $z=f(x,y)$ and the plane $z=\frac{3709}{2000}$, don't we?
Can we do that? (Wondering)

Btw, should the constant be $\frac{3709}{2000}$ or $\frac{1374}{2000}$? (Nerd)
mathmari said:
2. Give the graph of the below functions in Geogebra and find the countour lines $f(x,y)=c$ where $c$ is in the interval $[0,10]$ and each contour line has to have distance from the next one $0.4$.
  • $f(x,y)=\cos (xy)$
  • $f(x,y)=\frac{2}{\sqrt{x^2+y^2}}+\frac{2}{\sqrt{(x-1)^2+y^2}}$

Do we use for that the command "Sequence(\cos (xy)=c, c, 0, 10)" ?

We can use $\operatorname{Sequence}$ yes.
We'll have to specify an object that actually represents a curve though.
And shouldn't we specify a step size as well? (Wondering)
 
  • #3
Klaas van Aarsen said:
A contour line is a curve on a surface $z=f(x,y)$ for a fixed $z$ isn't it? (Wondering)

But if we specify $y-x^2-1=\frac{1374}{2000}$, we do not get such a curve do we?
Instead we are getting a different surface.
Makes sense, because we have effectively specified an equation in x and y without specifying z.
So Geogebra shows a surface that satisfies the equation for x and y, and shows it for any z.
It's a parabolic cylinder. (Worried)

I think that instead we need the intersection of the surface $z=f(x,y)$ and the plane $z=\frac{3709}{2000}$, don't we?
Can we do that? (Wondering)

Btw, should the constant be $\frac{3709}{2000}$ or $\frac{1374}{2000}$? (Nerd)

Oh it should be $\frac{3709}{2000}$ and not $\frac{1374}{2000}$, the second one was a typo. (Tmi) So do you mean the following?

View attachment 9598

(Wondering)
 

Attachments

  • intersect.JPG
    intersect.JPG
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  • #4
mathmari said:
So do you mean the following?

Yep. (Nod)
 
  • #5
Klaas van Aarsen said:
Yep. (Nod)
Ok, great! So 1. is done.

Let's consider question 2.

Do we maybe use the command "Sequence(Intersect(f,g), c, 0, 10, 0.4)" where $f(x,y)=\cos (xy)$ and $g(x,y)=c$ ? (Wondering)
 
  • #6
mathmari said:
Let's consider question 2.

Do we maybe use the command "Sequence(Intersect(f,g), c, 0, 10, 0.4)" where $f(x,y)=\cos (xy)$ and $g(x,y)=c$ ?

Well... does it work? (Wondering)

Your f is not actually the intended surface in 3D is it? (Worried)
 
  • #7
Klaas van Aarsen said:
Well... does it work? (Wondering)

Your f is not actually the intended surface in 3D is it? (Worried)
I tried the following, but something is wrong:

View attachment 9599

What do I have to change? (Wondering)
 

Attachments

  • intersection.JPG
    intersection.JPG
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  • #8
mathmari said:
I tried the following, but something is wrong:

What do I have to change?

The $g: z=c,\,0\le c\le 10$ doesn't seem to be understood. (Worried)

The $c$ should really be tied to a $\operatorname{Sequence}$.

How about $\operatorname{Sequence}(\operatorname{IntersectPath}(f,z=c), c, 0, 10, 0.4)$? (Wondering)
 
  • #9
Klaas van Aarsen said:
The $g: z=c,\,0\le c\le 10$ doesn't seem to be understood. (Worried)

The $c$ should really be tied to a $\operatorname{Sequence}$.

How about $\operatorname{Sequence}(\operatorname{IntersectPath}(f,z=c), c, 0, 10, 0.4)$? (Wondering)

Ahh ok! With this command we get:

View attachment 9600 For the other function $f(x,y)=\frac{2}{\sqrt{x^2+y^2}}+\frac{2}{\sqrt{(x-1)^2+y^2}}$ we get:

View attachment 9601

(Malthe)
 

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  • cos_c.JPG
    cos_c.JPG
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  • f2_c.JPG
    f2_c.JPG
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  • #10
mathmari said:
Ahh ok! With this command we get:

For the other function $f(x,y)=\frac{2}{\sqrt{x^2+y^2}}+\frac{2}{\sqrt{(x-1)^2+y^2}}$ we get:
(Malthe)

Nice! (Happy)
 
  • #11
Klaas van Aarsen said:
Nice! (Happy)

Thank you for your help! (Yes)
 

FAQ: Explore Contour Lines in Geogebra: Drawing and Finding Functions

1. What is Geogebra?

Geogebra is a free and multi-platform dynamic mathematics software that allows users to visualize and explore mathematical concepts, including graphs, geometry, algebra, and calculus.

2. How do I draw contour lines in Geogebra?

To draw contour lines in Geogebra, first, create a new graph by clicking on the "Graphing" icon on the toolbar. Then, use the "Function" tool to enter the desired function, and click on the "Contour" button on the toolbar. Select the function and the desired number of contour lines, and click "OK" to draw the contour lines.

3. Can I find the equation of a function using contour lines in Geogebra?

Yes, you can find the equation of a function using contour lines in Geogebra. After drawing the contour lines, right-click on the line and select "Show Label." This will display the equation of the contour line.

4. How do I change the interval of contour lines in Geogebra?

To change the interval of contour lines in Geogebra, double-click on the contour line to open the "Object Properties" window. Then, go to the "Advanced" tab and change the "Contour Step" value to the desired interval.

5. Can I export the contour lines as an image or a file in Geogebra?

Yes, you can export the contour lines as an image or a file in Geogebra. After drawing the contour lines, right-click on the graph and select "Export." Choose the desired file format and save the image or file to your computer.

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