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Two involutes (red) of a parabola. In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve.
Sep 12, 2020 · When we talk about a straight line : y = mx + b y = m x + b. a line is parallel to another if their m m is the same (disregarding the b b), is that right? What happens when we talk about a curve such as: y = nx2 + mx + b y = n x 2 + m x + b.
The red curve is parallel in two ways to the blue curve, and self-parallel. A similar notion is the notion of contour line of the function "distance (of a point on the plane) to the curve", called distance curve (or line).
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. It generalises the concept of parallel (straight) lines.
For the expression of the parallel curve, we have to consider and not where is the normal vector (the vector is defined so that the torsion cancels): A horopter curve (in blue) and a curve of the type. The "crossties" are indeed perpendicular to the blue curve, but not to the red one.
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: Parallel Surfaces
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Jul 27, 2023 · Left: the red curve is the evolute of the blue one, and the blue curve is an involute of the red one. Right: the evolute of an ellipse. The four cusps of the evolute correspond to the two minima and two maxima of the curvature of the ellipse.
