- Dec 22, 2023
The conformal map w(z) transforms the trajectory with energy −B in potential U(z):=A∣dw/dz∣2 into the trajectory with energy −A in potential V(w):=B∣dz/dw∣2. I will prove this beautiful result and show some implications of it.
- Nov 19, 2023
I show the latest Mastodon post in my website hosted on GitHub Pages, and it does not require JavaScript on the client side. How do I do that?
- Nov 9, 2023
For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an m-fold symmetry is compatible with translational symmetry is the same as whether φ(m)≤2.
- Nov 6, 2023
If you have not noticed, the equations on my blog are now rendered server-side. This change makes it possible for those who turn off JavaScript on their browsers to see the equations. I also updated the theme from Minima v2 to Minima v3.
- Oct 31, 2023
“It’s the weekend and you’ve just completed a seance with friends. After communing with the dead, you realize a mysterious message was left behind.” What is the decoded message? Use your Ruby skills to find out!
- Oct 18, 2023
When someone asks you why it is −i here instead of i or the other way around, you can say that this is just a convention. My professor of quantum mechanics once asked the class similar a question, and I replied with this letter.
- Sep 29, 2023
It has been a pain setting up Overleaf on my own server. I have finally figured it out and I am sharing my notes here.
- Sep 17, 2023
I have been using Linux and self-hosting for over a year now. Overall, I would like to say that it is rather satisfactory and that I will continue to use Linux as my daily driver in future. Thinking of that, I felt a little bit nostalgic about my old computers. So I decided to write an article about my old computers and my experience of daily driving Linux now.
- Sep 8, 2023
In order to build a better player community for the rhythm game Lyrica, I created a new rhythm game called Sunniesnow. Learn more about Sunniesnow by joining our Discord server.
- May 9, 2023
Suppose there are n distinguishable boxes and k indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains m balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit n,k→∞ with k/n fixed, the distribution tends to be a geometric distribution.