![How to estimate the value of $e$. [closed]](https://news.conceivablytech.com/uploads/how-to-estimate-the-value-of-e-closed_720.jpg)
news
How to estimate the value of $e$. [closed]
I am currently studying how to estimate $e$. To solve this problem I use these methods discuss below: Method 1: We know that $e^x = 1 + \dfrac{x}{1!} + \d...
Apr 20, 2026
Archive: News
news
How to parametrize a curve by its arc length
I am reading on Wikipedia that ''...Any regular curve may be parametrized by the arc length (the natural parametrization) and...'' I k...
Apr 20, 2026
news
What is the significance of the mirror numbers?
I'd like to hear insights and theory of the mirror numbers and their possible significance in mathematics and geometry. With mirror numbers I mean th...
Apr 20, 2026
news
When exactly is a compact complex manifold algebraic?
It is well known that a necessary and sufficient condition for a compact Kähler manifold $\mathcal{X}$ to be a projective algebraic variety is that it adm...
Apr 20, 2026
news
Is there a way to write this expression differently: $\arctan 1/(1+n+n^2)$?
$$ \arctan\left(\frac{1}{1+n+n^2}\right)$$ My professor wrote this as $$\arctan(n+1) - \arctan(n)$$ I don't understand how this expression is right?
Apr 20, 2026
news
Introductory texts on manifolds
I was studying some hyperbolic geometry previously and realised that I needed to understand things in a more general setting in terms of a "manifold" whic...
Apr 20, 2026
news
How to find the imaginary roots of polynomials
I'm looking for a simple way to calculate roots in the complex numbers. I'm having the polynomial $2x^2-x+2$ I know that the result is $1/4-$($\...
Apr 20, 2026
news
Is there a deeper understanding of the derivative of sin(x) = cos(x)?
Recently I showed my students how to prove that the derivative of $\sin(x) = \cos(x)$, using the limit definition of the derivative, trigonometric identit...
Apr 20, 2026
news
$(2, 1)$ is a point on the graph of $y = f(x)$. Find the corresponding point on the graph $y = 0.3f(5(x-3))$
I took the approach I saw in my class: $$y = 0.3f(5(x-3)) = 0.3f(5x-15)$$ $$(x, y) \mapsto (5x-15, 0.3y)$$ $$(2, 1) \mapsto (5(2)-15, 0.3(1)) = (-5, 0.3)$...
Apr 20, 2026
![Why is $i^2$ not equal to $1$? [duplicate]](https://news.conceivablytech.com/uploads/why-is-i-2-not-equal-to-1-duplicate_720.jpg)
news
Why is $i^2$ not equal to $1$? [duplicate]
I've only recently started learning about imaginary numbers, and there is one thing I cannot really wrap my head around: $i^2 = i*i = {\sqrt{-1}} * {...
Apr 20, 2026
