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Sep 12, 2020 · 2. Two curves are parallel if at any point you draw a line perpendicular to the tangent line and passes through the point of tangency (the normal line), the normal lines are all parallel, at any point along the curve, and the distance between the line's points of intersections with the two curves are all the same.
Opposite, animation of a normal line rolling without slipping on the evolute, drawing a parallel with cusp (in red), which is one of the involutes of the evolute (in green). The parallel curves of a curve are the curves , parallel of index a of , obtained by algebraically copying a "length" a from the points on on the oriented normal; in other ...
Parallel curve. Parallel curves of the graph of for distances. Two definitions of a parallel curve: 1) envelope of a family of congruent circles, 2) by a fixed normal distance. The parallel curves of a circle (red) are circles, too. A parallel of a curve is the envelope of a family of congruent circles centered on the curve.
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It just means at right angles (90°) to. The red line is perpendicular to the blue line: Here also: (The little box drawn in the corner, means "at right angles", so we didn't really need to alsoshow that it was 90°, but we just wanted to!) Try for yourself:
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. (They also point in the same direction). Just remember:
Question: What is the difference between perpendicular and parallel? Answer:90 degrees (a right angle) That's right, when we rotate a perpendicular line by 90° it becomes parallel (but not if it touches!) Likewise, parallel lines become perpendicular when one line is rotated 90°.
Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases:
The curves (G 1) and (G 2) are parallel if we can determine current points M1 and M2, respectively, such that and . For an initial curve with current point , a parallel is a set (G a) of points where , the angle being the torsion angle (see the notations). The surface area of the strip between two corresponding arcs of (G 0) and (G a) is equal ...
3 days ago · Identify the conditions for parallel lines. Lines are parallel if they have the same slope and will never intersect. Analyze the given lines (blue, red, and green) for their slopes.
The symmetric image of a curve with respect to a curve is the locus of the symmetric images of the points on the curve with respect to the tangent to at a point M located on the normal to at . Therefore, it also is, in general, the second part of the envelope of the circles centred on and tangent to (each circle having two characteristic points).
