# Questions tagged [winding-number]

For questions about winding numbers. The winding number of a continuous curve counts how many times it "loops" around a given point.

8 questions
591 views

How could I explain mathematically, that the winding number of a closed curve $\gamma$ around $a$ ($a \notin \gamma$) gives always an integer value. $$W(\gamma,a)=\frac{1}{2\pi i} \int_{\gamma} \... 1answer 2k views ### cauchy theorem over cycles homologous to zero Definitions: i) A cycle \gamma is a finite sequence of continuous oriented closed paths in the complex plane. We denote \gamma = (\gamma_1,...\gamma_n) where \gamma_k are the closed paths of ... 1answer 205 views ### Showing Equality of Winding Numbers Let  w \in \Bbb C , and let  \gamma, \delta : [0,1] \rightarrow \Bbb C  be closed curves such that for all  t \in [0,1], |\gamma(t) - \delta(t)| < |\gamma(t) - w| . By computing the winding ... 2answers 443 views ### Determine the Winding Numbers of the Chinese Unicom Symbol I'm practicing with Winding Numbers, and encountered an interesting example. You might be familiar with this liantong symbol, the logo of China Unicom: Suppose we make this into a fully closed and ... 2answers 850 views ### Show f has a fixed point if f\simeq c I have the following problem: Show that if f:S^1\to S^1 is a continuous map, and f is homotopic to a constant, then \exists p\in S^1 : f(p)=p. My approach is to show that if for all p, \  ... 1answer 237 views ### Limit \lim_{x\rightarrow x_0, x\in M} \int_{\partial M} \frac{1}{||y-x||} n_y \cdot \nabla_y \frac{-1}{||y-x||} dS_y Ok I had a question I think I can almost answer it but I miss one step: Let \partial M be a closed surface in \mathbb{R}^3, x_0 \in \partial M than show this limit:$$\lim_{\substack{x\...
$\def\RR{\mathbb{R}}$Let $S^1$ be the circle and let $\gamma : S^1 \to \RR^2$ be a smooth injective map with $\gamma'(t)$ everywhere nonzero. What is the easiest way to show that $t \mapsto \gamma'(t)$...