« first day (2105 days earlier)      last day (703 days later) » 

10:25 AM
A new tag .
1
Q: Prove that there exists an another path $g$ with the same image as $f$ but length of $g = tL \forall t\in [0,1]$ where $L$ is the length of $f$

MathManTheorem: Suppose $(X,d)$ is a metric space and $f:[0,1] \rightarrow X$ is a path in $X$ with no-zero finite length $L$. Then, there exists a path $g:[0,1] \rightarrow X$ from $f(0)$ to $f(1)$ that has the same image as $f$ and satisfies $lth_t(g) = tL ~\forall ~t \in [0,1]$. In particular $g$ is ...

 

« first day (2105 days earlier)      last day (703 days later) »