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In my procrastination, I've been trying to understand some basic topology which started with the definition of topological spaces, which I pretty much understand with the definition via open sets on ...

If a constant current flows through a superconducting ring, then when the external magnetic field changes, the current in it will change. If a charged body rotates, its angular velocity will change. ...

In Chapter 10 Section "Simplexes and Chains" Rudin introduces the concept of an affine oriented $k$-simplex $\sigma = [\mathbf p_0, \ldots, \mathbf p_k]$ with $\mathbf p_i \in \mathbb R^n$ ...

Our organization has internal GitHub repositories. We use .NET. We would like to keep production secrets out of source control. At the moment, the developers are aware of the production secrets, but ...

This problem is from the undergraduate olympiad "Elon Lima". Let $f_1(x) = x^2 + 4x + 2$ and let $f_{n+1}(x) = f(f_n(x))$ for $n \geq 1$. Let $s_n$ be the sum of coefficients of even power ...

In the 1980 movie The Sea Wolves, why is this German seafarer doing whatever he is doing? His actions are driving me up the wall. Why is he using this method to try to ...

We now almost invariably use 0123456789ABCDEF as our hexadecimal digits, as popularised by the IBM 360, but one of the earliest machines to use hexadecimal, the first ILLIAC, used KSNJFL for 1010₂ – ...

It seems clear at this point that AI will change mathematics in many ways and we should be well-prepared for it. However, reading recent trending posts about Math and AI on social media, blogs and ...

At the end of the original Back To The Future, Doc returns from the future with his hover-converted DeLorean (Yeah, I know, spoilers for a 41 year old movie!) Did Doc Brown pay someone to do the ...

I started with the classical idea that a circle can be approximated by regular polygons with an increasing number of sides. As the number of sides grows, the polygon visually becomes closer and closer ...

My Kohler toilet has a separate tank and bowl that are clamped together with two bolts. So, I have no access to the underside of the tank, because of the design, and how close it is to the wall. ...

In Acts 19:13–16, the sons of Sceva attempt to cast out an evil spirit by invoking “Jesus whom Paul proclaims,” and the spirit responds: “Jesus I know, and Paul I recognize, but who are you?” (Acts ...

Suppose there is a family of four living in Maryland: A mother, a father, and two adult children. The parents have significant jointly-owned assets. It seems likely that the mother and two children ...

When we draw a large arrow on the curve, the arrow not always along the curve. pts = {{0, 0}, {1, 5}, {2, -1}, {3, 0}}; Graphics[{Arrowheads[{{.1, .43}}], Arrow@BezierCurve[pts]}] I want the filled ...

This was asked before, but no answer was given. I would like to give a name to a manifold that can be covered by a single coordinate chart. Something other than "coordinate chart". In the ...

I'm using Debian 13 LXDE with Virtual Machine Manager installed. Recently I noticed that I can Copy & Paste across host and VMs by default. However I'm pretty sure that in older versions of Debian ...

Take two concentric equilateral triangles of sizes k and 3n-k for 0 < k < 3n. Orient them in opposite directions, say up and down. Consider the shapes obtained by taking the intersections of the ...

Find the missing word: Input Output Cannot Nebula Observe Kool Affectionate Solver Coiled ______

The answer is a year. Text version: U L W A T V Z D W D Q R M F F Y R T C J Y X P L O T P C A Y B F H X P N S E V Q K O A L E A G X O E U M L L N T B I U F V U Z G S O S R L K N T I S O E T N Q A Q L ...

First time applying drywall mud and it seems like I overapplied. I had watched a number of YouTube videos and had taken notes on the steps I needed to take, but I couldn't really execute properly. Pic ...