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- The red curve is parallel in two ways to the blue curve, and self-parallel.
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.
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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 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. It can also be defined as a curve whose points are at a constant normal distance from a given curve. [1]
The red curve is the symmetric image of the blue one with respect to the green one. Some properties: If is a line, we get, of course, the classic axial symmetry. Like this latter symmetry, the symmetry is "in general" involutory: if there is a one-to-one correspondence between and then the symmetric image of is .
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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.
