Intereting Posts

Making an infinite generating function a finite one
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
Polynomial boundaries
Proper inclusion between open ball, closure of open ball and the closed ball in a metric space
Find all real real functions that satisfy the following eqation $f(x^2)+f(2y^2)=$
Topology such that function is continuous if and only if the restriction is.
Transformations from n-sphere coordinates to cartesian coordinates.
Analogies between finite groups and Lie groups
Is $x/x$ equal to $1$
A conformal geodesic map must be a scaled isometry?
$k$-rational points of a scheme over $K$
Intersection of kernels and linear dependence of functionals
Uncountably many points of an uncountable set in a second countable are limit points
Distinguishing between symmetric, Hermitian and self-adjoint operators
Do there exist vector spaces over a finite field that have a dot product?

I know that this is a very simple question, but I am stuck at the very last part of this process and can’t find the solution elsewhere (I figured I’d find it on this site, but I didn’t see it).

I have an object that is colliding with a circle and I need it to deflect properly, like this:

I know the coordinates of the center of the circle and the object when it is on the circle’s perimeter. I know the direction that the object is traveling on contact and can calculate the direction to the center (pointing inwards).

From similar questions, I know that the tangent line is perpendicular to the radius line I calculate. But, I’m not sure where to go after that. I need to calculate the new direction of the object in degrees, but my idea $\theta = \theta + 2(radiusline – \theta)$

, where $radiusline$ is the vector pointing towards the center, is inaccurate.

- prove that line bisect section
- How to show that any rectangle in ellipse must be oriented parallel to axes?
- Detecting polygon self intersection
- Finding an unknown angle
- How many sides does a circle have?
- If $\gamma$ is spherical, then the equation $\frac{\tau}{\kappa}=\frac{d}{ds}(\frac{\dot{\kappa}}{\tau \kappa^2})$ holds.

What is the proper formula for this deflection?

- Height of Cylinder inscribed in Sphere
- Does the ternary dot product have any geometric significance?
- How to find where $3$ lines intersect.
- Find the approximate center of a circle passing through more than three points
- Covering the plane with disks
- Can a tetrahedron lying completely inside another tetrahedron have a larger sum of edge lengths?
- Can I represent groups geometrically?
- Heronian triangle Generator
- Average Degree of a Random Geometric Graph
- Do rotations about any three non-collinear axes generate $SO(3)$?

$$\begin{align}

\vec N & = \text{normal at point of incidence}=-a \hat{\mathbf{i}}-b \hat{\mathbf{j}} \\

\vec V & = \text{incident vector}=u \hat{\mathbf{i}}+v \hat{\mathbf{j}} \\

\vec R & = \text{reflected vector}=c \hat{\mathbf{i}}+d \hat{\mathbf{j}} \\

\end{align}$$

$$\begin{align}

\text{using}\ \vec R =\vec V -2\vec N(\vec V \cdot \vec N)&={u \choose v}-2{-a \choose -b}\left[{u \choose v}\cdot {-a \choose -b}\right]\\

&\\

&={u \choose v}-2(au-bv){-a \choose -b}\\

&={u+2a^2u-2abv \choose v+2a^2u-2b^2v} \equiv {c \choose d}\\

\end{align}$$

Hence $\vec R=(u+2a^2u-2abv)\hat{\mathbf{i}}+(v+2a^2u-2b^2v)\hat{\mathbf{j}}$

- Do people study “ring presentations”? Is this a dumb question?
- How do extension fields implement $>, <$ comparisons?
- Entropy of a natural number
- Proving statement – $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
- Surface Element in Spherical Coordinates
- which of the following metric spaces are complete?
- Find all primes such that $a^2+b^2=9ab-13$.
- What's the right moment to learn Set Theory?
- What is the distribution of sum of a Gaussian and a Rayleigh distributed independent r.v.?
- What is the intuition behind the name “Flat modules”?
- Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
- Curvature of given metric space
- If $=n$, is it true that $x^n\in H$ for all $x\in G$?
- Prove that: $\sup_{z \in \overline{D}} |f(z)|=\sup_{z \in \Gamma} |f(z)|$
- Infiniteness of non-twin primes.