I am trying to work out if the centre of rotation of a measured sphere is actually at 0,0 or slightly offset from the centre. The situation is as follows:...
Published: Sep 01, 2026
I have been reading about the mathematics behind Perlin noise, a gradient noise function often used in computer graphics, from Ken Perlin's presentat...
Published: Sep 01, 2026
How should one solve the following integral? $$\int \tan^2(x) \sec (x) \ dx$$ I can't think of any substitutions to be made involving $\tan^2(x)=\sec...
Published: Sep 01, 2026
I have no idea how to start these problems. How does one get the original function given the derivative of the function? I would appreciate it if someone ...
Published: Sep 01, 2026
I'm basically trying to solve the opposite of the brachistochrone problem. You know how the brachistochrone is the shortest path between two points A...
Published: Sep 01, 2026
Wikipedia says 'The difference between left and right actions is in the order in which a product like $gh$ acts on $x$. For a left action $h$ acts fi...
Published: Sep 01, 2026
Mariano mentioned somewhere that everyone should prove once in their life that every matrix is conjugate to its transpose. I spent quite a bit of time on ...
Published: Sep 01, 2026
Let $f(x) = x^3-x^2–3x–1$ and $h(x)=\dfrac{f(x)}{g(x)}$ where $h(x)$ is a rational function such that (a) it is continuous every where except when $x=– 1$...
Published: Sep 01, 2026
For a semisimple Lie Algebra $\mathfrak{g}$ with Cartan Subalgebra $\mathfrak{t}$, let $V(\lambda)$ be the unique irreducible highest weight module with h...
Published: Sep 01, 2026
I have two circles noted as $A$ and $B$. Each of these circles has known positions $\vec{P_A}$ and $\vec{P_B}$ with radii $r_A$ and $r_B$. I need to find ...
Published: Sep 01, 2026