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In this case, one gets a parallel curve on the opposite side of the curve (see diagram on the parallel curves of a circle). One can easily check that a parallel curve of a line is a parallel line in the common sense, and the parallel curve of a circle is a concentric circle.
Jan 10, 2018 · Concentric circles vs. Parallel circles. I was recently reading about parallel lines which by definition are lines on the same plane which never meet and are equidistant. I came across a piece of text where the concept of parallel lines was also extended to curves which is all right.
A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve.
Sep 23, 2010 · If you drop the "lines" requirement and use that definition, then, yes, concentric circles are "parallel" but then so are any circles that do not intersect, or any line segments that do not intersect, whatever their angular orientation, any curves that do not intersect, etc.
Feb 9, 2018 · The most elementary example of parallel curves is given by the family of concentric circles. Except for trivial cases such as circles and lines, parallel curves may be quite different from the original curve as the offset gets larger. An example of this is given by the catenary.
- ParallelCurve
- 2013-03-22 17:13:10
- 2013-03-22 17:13:10
- parallel curve
Apr 8, 2009 · Straight lines not intersecting is a specific example of parallel, while there are many examples of curves that can be considered parallel, such as concentric circles. The defining characteristic of parallel is a constant distance between the lines or curves.
Oct 7, 2010 · Concentric circles are parallel curves, but not parallel lines, because you can't perfectly place a section of the smaller circle onto a section of the larger circle and have them fit. The shortest distance between two points is always a straight line.
