How Do You Find the Curvature at (2, 4, -1)?

  • Context: MHB 
  • Thread starter Thread starter carl123
  • Start date Start date
  • Tags Tags
    Curvature Point
Click For Summary
SUMMARY

The curvature at the point (2, 4, -1) can be determined using the parametric equations x = 2t, y = 4t^(3/2), and z = -t^2. To find the curvature, one must compute the first and second derivatives of the position vector and apply the curvature formula from differential geometry. Referencing Pauls Online Notes provides additional examples and methods that clarify the curvature calculation process.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of calculus, specifically derivatives
  • Familiarity with curvature formulas in differential geometry
  • Ability to interpret results from examples in Pauls Online Notes
NEXT STEPS
  • Study the curvature formula in differential geometry
  • Practice finding derivatives of parametric equations
  • Review examples of curvature calculations from Pauls Online Notes
  • Explore applications of curvature in physics and engineering
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable calculus and differential geometry, as well as educators seeking to enhance their teaching materials on curvature.

carl123
Messages
55
Reaction score
0
Find the curvature at the point (2, 4, −1).


x = 2t, y = 4t3/2, z = −t2
 
Physics news on Phys.org
Please post your work so far, and that will help us help you!
 
carl123 said:
Find the curvature at the point (2, 4, −1).


x = 2t, y = 4t3/2, z = −t2

Hi carl123,

What have you tried? Here's some similar examples from Pauls Online Notes. If you read through them surely you'll know the method of finding the curvature.

Pauls Online Notes : Calculus III - Curvature
 

Similar threads

Undergrad Curvature of 3D Graph on Point w/ Directional Vector
  • · Replies 3 ·
Replies
3
Views
2K
MHB How Do You Calculate the Radius of Curvature for Complex Curves?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Finding roots of this particular polynomial
  • · Replies 4 ·
Replies
4
Views
2K
MHB 13.4.7 Find the curvature of the curve r(t).
  • · Replies 14 ·
Replies
14
Views
4K
High School Arithmetic mean of an infinite number of points?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Principal and Gaussian curvature of the FRW metric
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
Graduate How to Find Critical Points of function f(x,y,z)
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Find f(z) given f(x, y) = u(x, y) + iv(x,y)
  • · Replies 8 ·
Replies
8
Views
956
Undergrad ##f(2x)=f^2(x)-2f(x)-1/2## then find ##f(3)##
  • · Replies 17 ·
Replies
17
Views
3K