Results 1 to 4 of 4

Math Help - 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
    3,110
    Thanks
    2
    Have you considered the radius, the value of \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
    11,548
    Thanks
    539
    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:
    . . (x-1280)^2 + (y-800)^2 \:=\: 422500
    The center of the circle is: . C(1280,800)
    The radius is: . r \:=\:650


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

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

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

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


    The arc length between P and Q is: . 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: . C(1280,800)
    The radius is: . r \:=\:650


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

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

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

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


    The arc length between P and Q is: . 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: November 30th 2011, 07:35 PM
  2. Euclidean distance between points
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 6th 2010, 11:21 AM
  3. Replies: 5
    Last Post: June 5th 2010, 03:01 PM
  4. Vertical distance between 2 points on a circle
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2009, 07:00 AM
  5. [SOLVED] MDS and Euclidean distance
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: December 9th 2006, 12:28 AM

Search Tags


/mathhelpforum @mathhelpforum