Calculating centre of rotation given point coordinates at different positions
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Calculating centre of rotation given point coordinates at different positions

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

Why is gradient noise better quality than value noise?
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Why is gradient noise better quality than value noise?

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 to solve $\int \tan^2(x) \sec (x) \ dx$? [duplicate]
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How to solve $\int \tan^2(x) \sec (x) \ dx$? [duplicate]

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

How do I find the original function given the derivative? [closed]
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How do I find the original function given the derivative? [closed]

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

What is the Brachistochrone curve with an initial velocity?
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What is the Brachistochrone curve with an initial velocity?

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

right group action
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right group action

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

Matrix is conjugate to its own transpose
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Matrix is conjugate to its own transpose

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 $h(x)=\frac{f(x)}{g(x)}$ where $h(x)$ is a rational function such that
general

Let $f(x) = x^3-x^2–3x–1$ and $h(x)=\frac{f(x)}{g(x)}$ where $h(x)$ is a rational function such that

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

Irreducible Dual Representation
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Irreducible Dual Representation

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

Find the angle of a tangent line between two circles
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Find the angle of a tangent line between two circles

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

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