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May 14, 2025, 14:58:53

After using computers for all so many years, for the first time, the Insert key was actually useful when I was editing a file. I always thought the only reason it exists is for causing small headaches when my dumb fingers accidentally touch it.

The key was used when I was editing a string in a binary file, and I wanted to make sure that the offsets of all the contents afterward were not affected.

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Articles

  • 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<0E<0 is u≔p2−p02p2+p02n^+2p0p2+p02p,\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 u\mathbf u is the position of the particle on 3-sphere (a 4-dimensional vector), p\mathbf p is the momentum of the original particle in Kepler problem, n^\hat{\mathbf n} is a vector perpendicular to the 3-dimensional hyperplane where p\mathbf p lies, and p0≔−2mEp_0\coloneqq\sqrt{-2mE}.

  • 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…

  • 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+e−CC0(T0−T)T+\mathrm e^{-\frac C{C_0}}\left(T_0-T\right), where TT is the initial temperature of the object, T0T_0 is the temperature of the hot water, CC is the heat capacity of the object, and C0C_0 is the heat capacity of the hot water.

  • 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.

  • 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.

  • 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.

  • 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).

  • Jun 13, 2020

    Drawing a heart using Joukowsky transformation

    Joukowsky transformation of a circle centered at (1,1)\left(1,1\right) of radius 11 is a curve resembling a heart.

  • May 31, 2020

    Generalization of Euler–Lagrange equation

    We may generalize Euler–Lagrange equation to higher dimensional optimization problems: find a function defined inside a region to extremize a functional defined as an integral over that region, with the constraint that the value of the function is fixed on the boundary of the region.

  • May 14, 2020

    View of the world (physically rather than philosophically)

    The view of the world… Physically! In this article, I tried to use mathematical language to describe models of the physical world. A view of the world should include: a space (actually spacetime) with some mathematical structure on it (whose points are events in the world), a symmetry principle describing the symmetry of the world, and a motion law to describe the physics and dynamics of the world. This article proposed models for Galilean, Einsteinian, and even Aristotelian worlds. Can you come up with even other worlds?

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