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Curvature of a 1d curve in a 2d or 3d space.

Is a curved line 1d or 2d. No, a curve can never be more than one dimensional. The slope of the curve becomes steeper as time progresses, showing that. The general form for algebraic.

This is a debated question among mathematicians. But putting a 1d thing into 2d or 3d space does not give it. You can just as well define 1d curves in 3d space.

Distance from an end point or chosen. A circle (just the points on it) has no area so it should. Motion can be in a straight line (1d), in a plane (2d), or space (3d).

I'm conflicted on whether a circle should count as 1d or 2d. We describe them as a mapping from the 1d or 2d parametric domain into the 2d or 3d affine space in which the curve or surface lies. This curve lies on the 2d plane, but is itself 1d.

So what are you working on that requires you to think. Likewise, $\vec r$ = $5t$$\hat i$ + $2t^2$$\hat j$ is a $2d$ motion,. A 2d trajectory can be seen in the motion of a ball rolling on a flat.

Is curve s considered to be 1d or 2d? It has only length and no width or height. It’s easy to see that it is a $1d$ motion, because its locus equation is a straight line.

For example, the motion of a train on. A curved line is a type of line that is not straight and is bent. A 1d trajectory can be seen in the motion of a pendulum swinging back and forth in a straight line.

Curve embedded in 2d: We know that the curvature of the. You can map your 3d space onto a 1d line via a 3d hilbert curve, then map the 1d line into 2d via a 2d hilbert curve.

By definition, a curve is a one dimensional object that can be represented by a single equation or function. In mathematics, a circle is a curved line and the area within that line is a disc. Ax + by + cz + 1 = 0.

Ax + by + 1 = 0. I have two lines of reasoning which give two different answers. The curve itself (whether that curve is a line or a circle or a tangled jumble) is 1d, the space it is embeded might be 3d.

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