Generalizing the Abel Theorem to higher order differential equations
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Generalizing the Abel Theorem to higher order differential equations

let $$y''+p(t)y'+q(t)y=g(t)$$ then By the Abel theorem wronskian equals to : $$W= c e^{\int p(t)dt}$$ Now We want to generalise this to a 3...

Published: Aug 21, 2026

Why arctan in radian mode and arctan in degrees mode are different?
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Why arctan in radian mode and arctan in degrees mode are different?

So I've been playing around with my calculator. In degrees mode with my casio calculator, I typed, "$\arctan(1)$" and got an answer of 45. In radian ...

Published: Aug 21, 2026

Equation of a rectangle
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Equation of a rectangle

I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere.

Published: Aug 21, 2026

Is this the right way to prove basic limit identities?
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Is this the right way to prove basic limit identities?

For example let's say I wanted to prove that: $$\lim_{x \to \infty} \frac{1}{x} = 0$$ Normally I would use epsilon-delta for such proofs but then I s...

Published: Aug 21, 2026

Integration of secant [duplicate]
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Integration of secant [duplicate]

$$\begin{align} \int \sec x \, dx &= \int \cos x \left( \frac{1}{\cos^2x} \right) \, dx \\ &= \int \cos x \left( \frac{1}{1-\sin^2x} \right) \, dx...

Published: Aug 21, 2026

Finding a regular 16-sided polygon whose vertices are lattice points
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Finding a regular 16-sided polygon whose vertices are lattice points

Find a regular equilateral and equiangular 16-sided polygon that has vertices that are lattice points. What is the minimum side length? Find the vertices ...

Published: Aug 21, 2026

Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$.
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Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$.

Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$. What I Tried: Here is a picture :- I ...

Published: Aug 21, 2026

Prove the FHHF theorem using as much abstract non-sense as possible
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Prove the FHHF theorem using as much abstract non-sense as possible

This is my second attempt to solve exercise 1.6H from Vakil: Assume $F$ is a covariant right-exact functor and show that we get a map $HF^i \rightarrow H^...

Published: Aug 21, 2026

What is the general formula for calculating dot and cross products in spherical coordinates?
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What is the general formula for calculating dot and cross products in spherical coordinates?

I was writing a C++ class for working with 3D vectors. I have written operations in the Cartesian coordinates easily, but I'm stuck and very confused...

Published: Aug 21, 2026

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"Taylor Series" analog for functionals?

For a function $f(x)$, it is possible to write it as a taylor series centered around a point $x=a$: $$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(a){(x-a)}^{n}}...

Published: Aug 21, 2026

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