Ulysses' trip

Latest post

Nov 1, 2025, 18:10:28

I have never bought a single device (laptop, monitor, phone, or tablet) with higher than 60 Hz of display refresh rate, except the most recent device I bought. This one very device has unsolvable dynamic FPS problems, just as what I was afraid of. It is settled. I will never buy devices with high refresh rates again until they finally exit the market.

Articles

Nov 8, 2022
The point on the circle farthest to two lines

Suppose $P$ is a point on the circle $\odot C$ . When is the sum of distances from $P$ to two edges of $\angle O$ extremal? It turns out to be related to angle bisectors (the intersections of $\odot C$ and the bisector of $\angle O$ or its adjacent supplementary angle are extremals), while the edge cases (at the intersections of $\odot C$ and edges of $\angle O$ ) are a little tricky: we need to use the bisectors to divide the plane into four quadrants, pick the two quadrants where the line intersecting $\odot C$ at $P$ lies, translate the region to make it center at $C$ , and see whether $P$ is inside the translated region.
- Categories: math
- Tags: elementary geometry, trigonometry, from zhihu
Nov 8, 2022
Typesetting math in emails

After some comparison among solutions, I use KaTeX to typeset math in my emails.
- Categories: programming
- Tags: jekyll, ruby, tex
Nov 7, 2022
Mapping from Kepler problem to free particle on 3-sphere

There is a canonical transform of the Kepler problem which is the same as the problem of motion of a free particle on 3-sphere. The explicit formula of the transform as well as some links about this topic is written in the article. The explicit formula for $E<0$ is $\mathbf u\coloneqq\frac{p^2-p_0^2}{p^2+p_0^2}\hat{\mathbf n}+\frac{2p_0}{p^2+p_0^2}\mathbf p,$ where $\mathbf u$ is the position of the particle on 3-sphere (a 4-dimensional vector), $\mathbf p$ is the momentum of the original particle in Kepler problem, $\hat{\mathbf n}$ is a vector perpendicular to the 3-dimensional hyperplane where $\mathbf p$ lies, and $p_0\coloneqq\sqrt{-2mE}$ .
- Categories: physics
- Tags: classical mechanics, canonical transformation, letter, kepler problem
Nov 6, 2022
Solving linear homogeneous ODE with constant coefficients

By using power series, we can prove that the problem of solving linear homogeneous ODE with constant coefficients can be reduced to the problem of solving a polynomial with those coefficients. This article illustrates this point in detail, but it uses a very awful notation…
- Categories: math
- Tags: calculus, linear algebra, combinatorics, ode, long paper, from zhihu
Nov 6, 2022
Thoughts on a middle school thermal physics problem

To heat an object with hot water, if we divide the water into more parts and use each part to heat the object one after another, the final temperature will be higher. If the number of parts tends to infinity, then the final temperature will tend to the limit $T+\mathrm e^{-\frac C{C_0}}\left(T_0-T\right)$ , where $T$ is the initial temperature of the object, $T_0$ is the temperature of the hot water, $C$ is the heat capacity of the object, and $C_0$ is the heat capacity of the hot water.
- Categories: physics
- Tags: calculus, number sequence, from zhihu
May 23, 2022
I created a community rhythm game called Dododo

I have created a community rhythm game called Dododo. It is a rhythm game with musical rhythm notations.
- Categories: update
- Tags: update, rhythm game, web
Aug 21, 2020
New website for MOIS Project (club)

I have built a website for our club called MOIS Project. It is a club related to music and band.
- Categories: update
- Tags: update
Jul 28, 2020
My activities in 2020 JDFZ Summer Session

JDFZ is hosting a summer session, where lectures covering a wide range of topics are held. Come and see what are my activities during this event.
- Categories: update
- Tags: update
Jul 5, 2020
New website for Little Turings (club)

I, the president and one of the founders of Little Turings, created a website to distribute information about it. The website is bilingual (Chinese and English).
- Categories: update
- Tags: update
Jun 13, 2020
Drawing a heart using Joukowsky transformation

Joukowsky transformation of a circle centered at $\left(1,1\right)$ of radius $1$ is a curve resembling a heart.
- Categories: math
- Tags: complex