0
votes
2answers
72 views

Supremum Definition in context of a Rectifiable/Differentiable Curve

I am trying to prove that if I have 2 paramterizations of the same curve $\gamma$ and $\sigma$ (i.e. there is continuous bijective map $\phi$ such that $\sigma = \gamma \circ \phi$) then if the curve ...
1
vote
1answer
35 views

Under what conditions does integrating the normal vector along a boundary make no sense?

So suppose you have an open, simply-connected, and bounded subset $D$ of $\mathbb{R}^2$ with the boundary $\partial D$. I am interested in the integral of the normal vector along the boundary, i.e., ...
2
votes
2answers
46 views

Parameterized curve describing trajectory of thrown object

We describe the trajectory of a thrown object (neglecting friction and similiar effects) with the curve $$k(t) = \left(v_0\cos(\beta)t,\,v_0\sin(\beta)t-\frac{g}{2}t^2\right)$$ with ...
0
votes
1answer
188 views

parametrizing quarter of a circle

I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the ...
3
votes
1answer
519 views

Summation of an Arithmetic, Parametric Sequence

I'm trying work on my ability to break complex patterns down, and in this case I'm trying to model the denominators of Lacsap's Fractions: I managed to get the sequence that represents the ...