updates
Calculating probabilities in horse racing!
I've seen a few similar threads to this on different forums but they don't seem to conclude to a satisfactory answer. My question is this: If yo...
Apr 15, 2026
Archive: Updates
updates
Volume of a rectangular prism's walls
Sorry if this is an obvious question... I have been trying to figure this out for a little while and come up with nothing... If I have a rectangular prism...
Apr 15, 2026
updates
Complex proof of the Fundamental Theorem of Algebra
I am self-studying Stein's Complex Analysis text, in which he has as proof for the Fundamental Theorem of Algebra. For some reason, something about i...
Apr 15, 2026
updates
What is the tangent at a sharp point on a curve?
How to know which line represents tangent to a curve $y=f(x)$ (in RED) ?From the diagram , I cannot decide which line to take as tangent , all seem to tou...
Apr 15, 2026
![Tetrahedron and Sphere [closed]](https://news.conceivablytech.com/uploads/tetrahedron-and-sphere-closed_720.jpg)
updates
Tetrahedron and Sphere [closed]
Could someone give and explicit homeomorphism between the tetrahedron with vertices $(0,0,0)$, $(1,0,0)$, $(0,1,0)$ and $(0,0,1)$ and the $2-$sphere? Thanks
Apr 15, 2026
updates
How do i prove that $\frac{1}{\pi} \arccos(1/3)$ is irrational?
How do i prove that $\frac{1}{\pi} \arccos(1/3)$ is irrational?
Apr 15, 2026
updates
Rational vs Irrational distribution
Imagine I draw a number line, and I took two points. What's the distribution of rational and irrational numbers between them? If I put it in a diagra...
Apr 15, 2026
updates
Solving differential equation $x^2y''-xy'+y=0, x>0$ with non-constant coefficients using characteristic equation?
Whenever you deal with non-constant coefficients you usually use Laplace transform to solve a given differential equation, at least that's how how I ...
Apr 15, 2026
updates
Derivative of the variance wrt $x_i$
As the title states, I want to find the derivative of $$\frac{1}{N}\sum_i (x_i - \mu)^2$$ w.r.t $x_i$ (note that $\mu$ is also another function of $x_i$, ...
Apr 15, 2026
updates
How do i find $(1+i)^{100}?$
How do I find $(1+i)^{100}$ without expanding $(1+i)$ 100 times? Is there a quicker way to do this? The hint was to find the modulus and argument of $1+i$...
Apr 15, 2026
