Deriving the Witch of Agnesi Curve

  • Context: Graduate 
  • Thread starter Thread starter IvanCow
  • Start date Start date
  • Tags Tags
    Curve deriving
Click For Summary
SUMMARY

The discussion focuses on deriving the parametrization and Cartesian equation of the Witch of Agnesi curve, a significant topic in differential geometry. The curve is defined mathematically and can be constructed using geometric principles, particularly Pythagoras' theorem. Participants emphasize the importance of understanding the geometric construction to grasp the derivation process effectively. The Wikipedia page on the Witch of Agnesi provides additional context and visual aids for better comprehension.

PREREQUISITES
  • Differential geometry concepts
  • Understanding of Cartesian equations
  • Familiarity with geometric constructions
  • Knowledge of Pythagoras' theorem
NEXT STEPS
  • Study the geometric construction of the Witch of Agnesi curve
  • Learn about parametrization techniques in differential geometry
  • Explore the mathematical properties of the Witch of Agnesi curve
  • Review applications of Pythagorean theorem in curve derivations
USEFUL FOR

Students and professionals in mathematics, particularly those studying differential geometry, as well as educators seeking to explain the Witch of Agnesi curve and its derivation methods.

IvanCow
Messages
2
Reaction score
0
Hello,
I have encountered an exercise in my differential geometry book: to derive the parametrisation and the cartesian equation of the curve witch of Agnesi.

To see how it is constructed please see:

http://en.wikipedia.org/wiki/Witch_of_Agnesi"

How would one derive the results? I am lost. Please help. Thanks.
 
Last edited by a moderator:
Physics news on Phys.org
From the geometric construction and Phytagora's theorem.
 

Similar threads

Celebrating Maria Gaetana Agnesi - Mathematician & Philanthropist
  • · Replies 2 ·
Replies
2
Views
9K
Graduate Calculating Lie Derivative for Case (ii)
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Using the derivative of a tangent vector to define a geodesic
  • · Replies 7 ·
Replies
7
Views
4K
Derivation for modified sine curve equations
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Understanding Metric Tensor Calculations for Different Coordinate Systems
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Algorithm to determine the roulette curve
  • · Replies 1 ·
Replies
1
Views
3K
MHB Janet's question at Yahoo Answers involving the Witch of Agnesi
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What Is the Genus of One-Dimensional Curves?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Looking for a good analytic geometry book
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Parametrizing a Complex Curve on a Torus Surface
  • · Replies 2 ·
Replies
2
Views
2K