Graphing Functions in n Dimensions, Parametric Equations

Click For Summary
SUMMARY

This discussion focuses on graphing functions in multiple dimensions, specifically linear functions represented in vector form as L = {p1 + t(p1-p2)|t∈R}. The conversation highlights the need for understanding how to graph polynomials and trigonometric functions using similar vector representations. Participants suggest starting with 2D examples, such as C = P + tV + t^2W, to visualize these concepts effectively. The discussion emphasizes the importance of linear algebra in understanding these graphing techniques.

PREREQUISITES
  • Linear algebra concepts, particularly vector representation
  • Understanding of parametric equations
  • Familiarity with polynomial functions
  • Knowledge of trigonometric functions and their properties
NEXT STEPS
  • Research how to graph polynomial functions in multiple dimensions
  • Explore the use of parametric equations for trigonometric functions
  • Learn about vector calculus and its applications in graphing
  • Study examples of 2D and 3D graphing techniques using software tools like GeoGebra
USEFUL FOR

Students and educators in mathematics, particularly those interested in linear algebra, graphing techniques, and anyone looking to deepen their understanding of multi-dimensional functions.

TheDemx27
Gold Member
Messages
169
Reaction score
13
So I was watching this video on Khan Academy, and it talks about graphing functions that have values in multiple dimensions. It shows how to represent a linear function in 3 dimensions with a set of vectors, L ={p1 + t(p1-p2)|t∈R} where p1 and p2 are vectors that lie on the line you want to graph. My question is: How would one go about graphing polynomials, or trigonometric functions?

The video was under the linear algebra category, but to be honest I don't know enough about linear algebra to determine whether or not this should go in that subforum.
 
Last edited:
TheDemx27 said:
My question is: How would one go about graphing polynomials, or trigonometric functions?

Having watched the video, I'd phrase your question this way:

A line can be represented in vector form as L = P + tV where P and V are constant vectors and t is a parameter. What curves can be represented using constant vectors and a parameter?

That's as good question. We could start by looking by plotting examples in 2D, like C = P + tV + t^2W just to see what they look like.
 

Similar threads

Undergrad Dimension and solution to matrix-vector product
  • · Replies 4 ·
Replies
4
Views
3K
High School Parametric Representation of Lines
  • · Replies 13 ·
Replies
13
Views
4K
Undergrad Comparing different scale factor functions in the same graph
  • · Replies 6 ·
Replies
6
Views
13K
MHB Dimension of Dirac Functionals in $V$: Find the Answer
  • · Replies 8 ·
Replies
8
Views
3K
Parametric Equation of a line, Conditions
  • · Replies 3 ·
Replies
3
Views
4K
MHB How do I find the Euclidean Coordinate Functions of a parametrized curve?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate What is the dimension of eigenspaces in a function-based linear transformation?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate C* algebras, states, finite graphs
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How to graph parametric equations?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What Is the New Dimension in Complex Number Graphs?
  • · Replies 19 ·
Replies
19
Views
4K