# Tagged Questions

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.

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### Plane integral for continuous curves

I'm trying to understand complex path integral $\int_C f(z)dz$ for continuous closed curve $C$. Is it necessary that $C$ is rectifiable and not just generally continuous? Do we get all the ...
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### Describe curves by words

I am trying to describe the general aspect of the following curves My ideas: The curves are continuous, and defined for positive values of x, and giving negative values. Have logarithmic growth (...
The problem in the following : given an algebraic curve $C$, it's well-known that a smooth projective model of $C$ can be construct as the set of discrete valuations $v$ on it's function field $\... 0answers 11 views ### Are involutes always regular? Suppose the curve$\alpha:I \rightarrow \mathbb{R}^2$is an involute of a regular curve. Does$\alpha'(t)\neq 0$hold for all$t\in I$? 1answer 18 views ### Is the evolute always a regular curve? [closed] Is the evolute always a regular curve? (that is, the tangent vector of this curve is nonzero at any time) 0answers 38 views ### Differentiable, Parametrized Curve for Trace$y = |x|$my professor gave practice problems for an upcoming midterm, and one is to find a differentiable parametrized curve with trace$y = |x|$with$-1 \leq x \leq 1$. My thinking is that I should find a ... 0answers 38 views ### Are all curves with equation of the form$(\xi x +n) \cdot x = \text{const}$circles? Let$x(t)=(x_1(t),x_2(t))$with$t\in [a,b]$be a smooth curve in$\mathbb{R}^2$and$\xi \in \mathbb{R}$such that $$(\xi x +n) \cdot x = \text{const}$$ Here$n$is the unit normal to the curve. Is ... 1answer 37 views ### Prove that for any piecewise smooth curve it is possible to find the parametrisation Prove that for any piecewise smooth curve it is possible to find the parametrisation$\phi$that is consistent with its length, ie. length of a curve segment between$\phi(a)$and$\phi(b)$is equal ... 1answer 38 views ### Geodesics on surface of revolution of regular curve I was recently presented with this in differential geometry stating the following: Let us define the regular curve on the XZ plane as:$ \gamma (t) = (sin(t)+2,0,t) $on XZ plane for$ t \in R $, ... 1answer 42 views ### Can a curve cross its asymptote infinitely many times? Can a curve cross infinitely many times its asymptote? If so, is there a special name for this behaviour? 2answers 50 views ### Can a surface of revolution be built from a self-intersected curve? I'm reading "Differential Geometry of Curves And Surfaces" of Manfredo Do Carmo. There's a point in his book about Surfaces of Revolution which confuses me a lot. Here is the part: The part ... 2answers 44 views ### Problem about curves. A particle is running along circumference$x^2+y^2=25\$
I'm considering a problem about curves. A particle is running along circumference $$x^2+y^2=25$$ with a costant modulus speed compliting a turn in 2 second. I need to determinate the acceleration in ...