Find the length of the curve r = cos^2(theta/2)

  • Thread starter Thread starter Manni
  • Start date Start date
  • Tags Tags
    Curve Length
Manni
Messages
42
Reaction score
0
Find the length of the curve r = cos^2(theta/2)

I'm hopelessly lost.
 
Physics news on Phys.org
consider a simpler case y=x^2 and what is the length from x=0 to x=10?

dlen = (dx*dx + dy*dy) ^ (1/2) based the pythagorian theorem

and dy= 2xdx

so dlen = ( dx*dx + 4x^2 dx*dx ) ^ (1/2) = (1 + 4x^2) dx

then integrate over x to get the solution

In your equation you must consider polar coordinates so that the dlen element is:

dlen = ( dr^2 + (r*dtheta)^2 ) ^ (1/2)

plugin for dr and r and integrate over theta to get the length
 
Thanks a lot, makes more sense! Forgive my ignorance by the way.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top