Conference rusure::math

954.0. "Cissoid of Diocles" by KAOA12::BARKLEY (Steve Barkley) Wed Oct 19 1988 00:18

	I'm currently taking a History of Mathematics course and
	the following question appears as one of the assignment
	questions (which is due TOMORROW).  Can anyone shed some
	light on this?
----------------------------------------------------------------------
	"Let a circle C roll along a line AB, beginning at O.  Let MN
	denote the diameter of C which is perpendicular to AB, where
	M is the point of contact, and let P denote the intersection
	of C and ON.  Prove that the locus of P is a cissoid of
	Diocles.  (MN, ON, and P all vary as C rolls; P is NOT a
	fixed point on C, nor is MN a fixed diameter of C)."

             -->  -->
                                                   N
             *******                        P   ***.***
       C   *         *                  _     +    |    *
          *        _  *-     -     -    .    *     |     *
          *      /    *         .            *     |     *
           *    |    *  .                     *    |    *
             ***.***                            *******
    A -------------------------------------------------------- B
                O                                  M

	Some extra information that may be hidden by the CRUDE
	diagram:
		- ON is a line segment (marked by ".")
		- the cissoid and line segment intersect at the "+"

                                          Thanks for any help,

                                               Steve Barkley

     Hint.  The line OPN is perpendicular to the line PM.
     
     Dan