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Questions tagged [plane-curves]

Plane curves are continuous (or smooth) functions $\gamma\colon I\to\mathbb R^2$ from a real interval to the plane. Sometimes also the image $\gamma(I)$ is called curve.

Plane curves are continuous (or smooth) functions $\gamma\colon I\to\mathbb R^2$ from a real interval to the plane. Sometimes the image $\gamma(I)$ is also called a curve.

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Finding POI's for the follow two curves

So I need to find the POI (point of intersection) of the following two curves: \begin{align*} r & = 1 + \cos \theta, \\ r & = 2 - 2\cos \theta. \end{align*} What I did was I just set both the equations equal to each other... $$1 + \cos \theta = 2 -…
Nick
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Quick question regarding wording of a homework question

Find the equation for the plane passing through the heads of the three given vectors (2, 2, 0) (−1, 2, 1) (1, 1, 4) Is this just another way of asking what is the plane passing through these points, or does "through the heads" mean something…
Luke
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A question about geometry of plane curve books

I can't study algebraic geometry yet, so before i learn that, yet i need a comprehensive treatment to the geometric theory of plane curves. i notice that the books refer to this subject either out of print thick one or not comprehensive thin books.…
Victor
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A 4th grade curve meets a line in one point with multiplicity 4

Suppose a 4th grade curve meets a line in one point with multiplicity 4. Example: the lemniscate $(x^2 + y^2)^2 = y^2 - x^2$ meets the line $x=y$ when the condition $x^4=0$ holds. This shows that line $x=y$ meets the lemniscate in one point $(0,0)$…
Gerard
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Isomorphism from $\mathbb{R}^2$ to $\mathbb{D}$ such that lines become circular arcs

I'm currently working on a hobbyist math project that require taking lines on an infinite plane, and projecting them onto a finite (euclidean) surface such that intersections are preserved. Does there exist an isomorphism from $\mathbb{R}^2$ to…
Ryan
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Find parametric vector equation ...

The plane $II_1$ has equation $ax+by+cz=0$ and the plane $II_2$ has Cartesian equation $ax+by+cz=d$. The two planes are parallel and$ II_1$ passes through the origin. Find a parametric vector equation for the position of the line which passes…
Heidi
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