The discussion revolves around determining the maximum and minimum values of the curvature for the polar curve defined by r = 3 + sin(θ). Participants are exploring the concepts of curvature in the context of polar coordinates and parametric equations.
Some participants are seeking clarification on the curvature formula and its application, while others express uncertainty about the methods discussed. There is a mix of understanding regarding the concepts of vectors and curvature, with some guidance provided on differentiating to find extrema.
Participants mention that their current studies focus on parametric equations and polar coordinates, indicating a potential gap in knowledge regarding vector calculus and curvature definitions. There is a lack of consensus on the approach to take, with various interpretations being explored.
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:[tex]\kappa=\frac{\left|\mathbf{r}'\times\mathbf{r}''\right|}{\left|\mathbf{r}'\right|^{3}}[/tex]
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.