[math-fun] Inverse cycloid problem ?
A cycloid is produced by a point on a circle as the circle rotates without slipping on a surface. What if we turn the problem around ? What curves can be produced by another curve rotating without slipping on a surface ? E.g., a semicircle is produced by a line segment "rotating without slipping" on a surface.
On 11/26/12, Henry Baker <hbaker1@pipeline.com> wrote:
A cycloid is produced by a point on a circle as the circle rotates without slipping on a surface.
I think this may have been intended to read something like: "A cycloid is the curve described by a point on a circle as the circle moves rigidly in the plane, while maintaining contact with a fixed line without slipping."
What if we turn the problem around ?
What curves can be produced by another curve rotating without slipping on a surface ?
E.g., a semicircle is produced by a line segment "rotating without slipping" on a surface.
But I'm afraid I still can't decipher this description ... WFL
On 11/26/2012 10:05 AM, Fred lunnon wrote:
On 11/26/12, Henry Baker<hbaker1@pipeline.com> wrote:
A cycloid is produced by a point on a circle as the circle rotates without slipping on a surface. I think this may have been intended to read something like:
"A cycloid is the curve described by a point on a circle as the circle moves rigidly in the plane, while maintaining contact with a fixed line without slipping."
What if we turn the problem around ?
What curves can be produced by another curve rotating without slipping on a surface ?
I assume he means something like a trochoid, a plane figure formed by joining three equal circular arc of pi/3 at their ends, rolling along a line without slipping. Brent
E.g., a semicircle is produced by a line segment "rotating without slipping" on a surface.
But I'm afraid I still can't decipher this description ... WFL
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Fred lunnon -
Henry Baker -
meekerdb