The discussion focuses on determining the maximum and minimum values of curvature for the polar curve defined by the equation r = 3 + sin(θ). Participants emphasize the necessity of finding the curvature using the formula κ = |r' × r''| / |r'|³. To identify extrema, users suggest differentiating the curvature and setting it equal to zero. The conversation highlights a lack of familiarity with vector calculus among some participants, indicating a need for foundational knowledge in parametric equations and polar coordinates.
PREREQUISITESStudents studying calculus, particularly those focusing on polar coordinates and curvature, as well as educators seeking to clarify these concepts for their students.
trap said:so do I derive the curve and let it equal to zero to find the maximum? how about the minimum? also...I don't really get how do you find the curvature of the curve?
apmcavoy said:\kappa=\frac{\left|\mathbf{r}'\times\mathbf{r}''\right|}{\left|\mathbf{r}'\right|^{3}}
here you can say r=<θ, 3+sinθ>
trap said:Sorry...I don't really get what you just typed, coz I don't think I have learned those in my course. We are currently doing parametric equations and polar coordinates. Is there an other approach to the question?
See Mathworld - Curvature. You're probably looking for the extrinsic curvature of a curve in the plane.trap said:so do I derive the curve and let it equal to zero to find the maximum? how about the minimum? also...I don't really get how do you find the curvature of the curve?
apmcavoy said:What I just typed was the vector form. Do you know about vectors from a previous course? Maybe precalc.?
hypermorphism said:See Mathworld - Curvature. You're probably looking for the extrinsic curvature of a curve in the plane.
trap said:yeah, something about the parametric, cartesian, polar equations are what we are learning. But I still don't get how to find the 'maximum' and 'minimum' values of the curvature.