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Jul 25, 2024, 01:46:46

After giving some thoughts, I think something like GitHub issues can be the ultimate form of a #socialmedia platform. One can conveniently refer to other issues using just owner/repo and issue number. One can use issue templates. One can use Markdown as well as inserting multimedia contents in comments. One can react with an emoji. These features easily beat Reddit and Mastodon. It only misses normal social platform features like exploration and tagging.

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Articles

  • Nov 9, 2022

    The image of a circular object through a thin lens

    The image of a circle with radius rr and centered at C(−2f,0)C\left(-2f,0\right) through a thin lens at x=0x=0 with focal length ff and centered at O(0,0)O\left(0,0\right) is a conic section with the focus being (2f,0)\left(2f,0\right), the directrix being line x=fx=f, and the eccentricity being rf\frac rf.

  • Nov 8, 2022

    The point on the circle farthest to two lines

    Suppose PP is a point on the circle ⊙C\odot C. When is the sum of distances from PP to two edges of ∠O\angle O extremal? It turns out to be related to angle bisectors (the intersections of ⊙C\odot C and the bisector of ∠O\angle O or its adjacent supplementary angle are extremals), while the edge cases (at the intersections of ⊙C\odot C and edges of ∠O\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 ⊙C\odot C at PP lies, translate the region to make it center at CC, and see whether PP is inside the translated region.

  • Nov 8, 2022

    Typesetting math in emails

    After some comparison among solutions, I use KaTeX to typeset math in my emails.

  • 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).

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