Search results
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).
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.
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.
- Perpendicular
- Parallel
- Perpendicular to Parallel
- Parallel Curves
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:
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.
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.
People also ask
Is a red curve parallel to a blue curve?
What is a parallel of a curve?
Are red and green curves parallel?
Are crossties perpendicular to a blue curve?
Is a parallel curve of a line a concentric circle?
How do you know if a curve is parallel?
May 28, 2023 · Curves often arise as the intersection of two surfaces. For example, the intersection of the sphere \(x^2+y^2+z^2=1\) with the plane \(y=x\) is a circle. The part of that circle that is in the first octant is the red curve in the figure below.
