Results 1 to 4 of 4

Thread: How do I measure the distance between two points on a euclidean graphed circle?

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    3

    How do I measure the distance between two points on a euclidean graphed circle?

    So I have a circle defined in a euclidean plane, how do I measure the distance along the circle between any two given points on the circle?



    The specific circle that I'm looking at right now is defined by the equation:

    (x-1280)^2 + (y-800)^2 = 422500




    thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Have you considered the radius, the value of $\displaystyle \pi$, and the proportion of the circle cut out by the wedge formed by the center and the two points?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, Egoist!

    So I have a circle defined in a euclidean plane.
    How do I measure the distance along the circle
    between any two given points on the circle?


    The specific circle that I'm looking at right now is defined by the equation:
    . . $\displaystyle (x-1280)^2 + (y-800)^2 \:=\: 422500$
    The center of the circle is: .$\displaystyle C(1280,800)$
    The radius is: .$\displaystyle r \:=\:650$


    Suppose the two given points are: .$\displaystyle P(x_1,y_1),\;Q(x_2,y_2)$

    Find the slope of $\displaystyle CP\!:\;\;m_1 \:=\:\frac{y_1-800}{x_1-1280}$

    Find the slope of $\displaystyle CQ\!:\;\;m_2 \:=\:\frac{y_2-800}{x_2-1280}$

    The angle $\displaystyle \theta$ between the two radii is given by: .$\displaystyle \tan\theta \:=\:\frac{m_2-m_1}{1 + m_1m_2}$
    . . Find $\displaystyle \theta$ in radians.


    The arc length between $\displaystyle P$ and $\displaystyle Q$ is: .$\displaystyle s \;=\;r\theta$

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2009
    Posts
    3
    Quote Originally Posted by Soroban View Post
    Hello, Egoist!

    The center of the circle is: .$\displaystyle C(1280,800)$
    The radius is: .$\displaystyle r \:=\:650$


    Suppose the two given points are: .$\displaystyle P(x_1,y_1),\;Q(x_2,y_2)$

    Find the slope of $\displaystyle CP\!:\;\;m_1 \:=\:\frac{y_1-800}{x_1-1280}$

    Find the slope of $\displaystyle CQ\!:\;\;m_2 \:=\:\frac{y_2-800}{x_2-1280}$

    The angle $\displaystyle \theta$ between the two radii is given by: .$\displaystyle \tan\theta \:=\:\frac{m_2-m_1}{1 + m_1m_2}$
    . . Find $\displaystyle \theta$ in radians.


    The arc length between $\displaystyle P$ and $\displaystyle Q$ is: .$\displaystyle s \;=\;r\theta$

    Thank you very much! BTW, as you can see, I'm new here, how do I "officially" thank you?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lebesgue measure of a manifold embedded in the euclidean space
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Nov 30th 2011, 07:35 PM
  2. Euclidean distance between points
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jun 6th 2010, 11:21 AM
  3. Replies: 5
    Last Post: Jun 5th 2010, 03:01 PM
  4. Vertical distance between 2 points on a circle
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 18th 2009, 07:00 AM
  5. [SOLVED] MDS and Euclidean distance
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: Dec 9th 2006, 12:28 AM

Search Tags


/mathhelpforum @mathhelpforum