Latest post

Jan 8, 2026, 10:32:08

My bike just decided to fail me again today by completely cutting off the chain and having it drop to the ground while I was riding it. Fortunately, I have a second bike that I can use in this very occasion. To be honest, the maintenance work required for the bike is exceeding my expectations. I have to fix some parts of it every year.

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Articles

  • Apr 11, 2020

    Snippet: O, ’tis too true!

    O, ’tis too true!

  • Apr 8, 2020

    The structure of a basic RM game

    In this article, I present minimal examples of a RM game. They only illustrate the basic concepts of how a RM game is structured and what is the running logic of it.

  • Mar 27, 2020

    The frequency assignment of musical notes

    This article explores the concept which I call the frequency assignment, which is a mapping from NN (the set of notes) to R+\mathbb R^+ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.

  • Mar 3, 2020

    Normal vectors of a scalar field

    This article gives the formula for the normal vectors of a surface defined by a scalar field on Rn\mathbb R^n. The normal vector of the graph of the function y=f ⁣(x)y=f\!\left(\mathbf x\right) at (x0,f ⁣(x0))\left(\mathbf x_0,f\!\left(\mathbf x_0\right)\right) is (∇f ⁣(x0),−1)\left(\nabla f\!\left(\mathbf x_0\right),-1\right). This also provides us a way to recover a scalar field from the normal vectors of its graph: normalizing the vectors so that the last component is −1-1, and then integrate the rest components.

  • Feb 29, 2020

    It is Feb 29 today!

    It is Feb 29 today. The date appears once for as long as 4 years!

  • Feb 9, 2020

    Monkey-patching graciously

    Monkey-patching is a powerful tool in programming. In this article, I used techniques of Ruby metaprogramming to define a series of methods def_after, def_before, etc. to help monkey-patching. They look graciously in that we can use it to shorten the codes for monkey-patching (avoiding aliasing and repeating codes).

  • Jan 26, 2020

    Amazing Siteleaf

    I have been using Siteleaf to manage my blog. It is just convenient and amazing.

  • Jan 25, 2020

    Hyperellipsoids in barycentric coordinates

    In this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.

  • Jan 6, 2020

    Use complex numbers as canonical variables

    In this article, I try exploring an idea: using complex numbers to combine pairs of canonical variables into complex variables: c≔αq+iβp\mathbf c\coloneqq\alpha\mathbf q+\mathrm i\beta\mathbf p. It turns out that we can write canonical equations dcdt=−2iαβ∂H∂c∗\frac{\mathrm d\mathbf c}{\mathrm dt}=-2\mathrm i\alpha\beta\frac{\partial\mathcal H}{\partial\mathbf c^*}, Poisson brackets {f,g}=−2iαβ(∂f∂c⋅∂g∂c∗−∂f∂c∗⋅∂g∂c)\left\{f,g\right\}=-2\mathrm i\alpha\beta \left(\frac{\partial f}{\partial\mathbf c}\cdot \frac{\partial g}{\partial\mathbf c^*}- \frac{\partial f}{\partial\mathbf c^*}\cdot \frac{\partial g}{\partial\mathbf c}\right), and canonical transformations ∂c∗∂c′∗=∂c′∂c,∂c∂c′∗=−∂c′∂c∗\frac{\partial\mathbf c^*}{\partial\mathbf c'^*}= \frac{\partial\mathbf c'}{\partial\mathbf c}, \frac{\partial\mathbf c}{\partial\mathbf c'^*}= -\frac{\partial\mathbf c'}{\partial\mathbf c^*} in these complex numbers. Finally, I show two examples of using them in real problems: a free particle, and a harmonic oscillator.

  • Jan 1, 2020

    Giving birth to my own blog

    This is my first blog! I will share interesting things in my life here.

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