Explore Contour Lines in Geogebra: Drawing and Finding Functions

  • Context: MHB 
  • Thread starter Thread starter mathmari
  • Start date Start date
  • Tags Tags
    Lines
Click For Summary

Discussion Overview

The discussion revolves around using Geogebra to draw contour lines for specific functions, particularly focusing on the function $f(x,y)=y-x^2-1$ and exploring commands for generating contour lines for other functions like $f(x,y)=\cos (xy)$ and $f(x,y)=\frac{2}{\sqrt{x^2+y^2}}+\frac{2}{\sqrt{(x-1)^2+y^2}}$. Participants seek to clarify the correct commands and methods for visualizing these contour lines.

Discussion Character

  • Technical explanation
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • Some participants propose using the command to plot $y-x^2-1=\frac{1374}{2000}$, but question whether this correctly represents a contour line.
  • Others argue that the correct approach involves finding the intersection of the surface $z=f(x,y)$ and the plane $z=\frac{3709}{2000}$.
  • There is a discussion about the appropriate command for generating contour lines in Geogebra, with suggestions including "Sequence(\cos (xy)=c, c, 0, 10)" and "Sequence(Intersect(f,g), c, 0, 10, 0.4)".
  • Participants express uncertainty about whether the commands used accurately represent the intended surfaces in 3D.
  • One participant suggests using "Sequence(IntersectPath(f,z=c), c, 0, 10, 0.4)" as a potential solution for generating contour lines.
  • There is a clarification regarding the constants used in the equations, with a consensus that $\frac{3709}{2000}$ is the correct value.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best command to use for generating contour lines, with multiple competing views and suggestions remaining throughout the discussion.

Contextual Notes

Participants express uncertainty about the correct syntax and functionality of commands in Geogebra, indicating potential limitations in their understanding of how to represent contour lines accurately.

mathmari
Gold Member
MHB
Messages
4,984
Reaction score
7
Hey! :o

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)
 
Physics news on Phys.org
mathmari said:
Hey! :o

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)
 
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
    57.8 KB · Views: 147
mathmari said:
So do you mean the following?

Yep. (Nod)
 
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)
 
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)
 
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
    94.7 KB · Views: 140
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)
 
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)
 

Attachments

  • cos_c.JPG
    cos_c.JPG
    123.1 KB · Views: 155
  • f2_c.JPG
    f2_c.JPG
    89.5 KB · Views: 143
  • #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)
 

Similar threads

MHB Region of continuity - Geogebra
  • · Replies 4 ·
Replies
4
Views
2K
MHB Tikz for f(x)=5x^2-2x and tangent line at 1,3
  • · Replies 5 ·
Replies
5
Views
3K
MHB What is the Graph of $f(x)=3\cos(\pi x-2)+5$ with Amplitude and Period?
  • · Replies 6 ·
Replies
6
Views
2K
Fixing the position of a number line in section
  • · Replies 2 ·
Replies
2
Views
2K
MHB Tikz for Gaussian Function: Enhance Your Figures with Custom Commands
  • · Replies 5 ·
Replies
5
Views
3K
LaTeX How Can I Color Different Sections of a Torus in LaTeX Using TikZ?
  • · Replies 1 ·
Replies
1
Views
4K
Slope of a mountain ridge (Gradient)
  • · Replies 5 ·
Replies
5
Views
2K
MATLAB Troubleshooting Best Fit Line and Distance Calculation in MATLAB
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Problem with calculating projections of curl using rotation of contour
  • · Replies 9 ·
Replies
9
Views
1K
MHB Probability of z > 1.28: Visualizing the Gaussian Curve
  • · Replies 2 ·
Replies
2
Views
2K