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I remember experiencing many rainy weekends and Mondays. To see whether this is a fact, I downloaded #weather data from #GHCND:USW00053152 from 2022-09-01 to 2024-05-01 and summed up the precipitations for each weekday.
It turns out that the total #precipitation for each weekday is (from Sunday to Saturday, in unit of mm): 239.0, 250.9, 212.9, 156.6, 172.0, 160.3, 219.8. Surprisingly we do have especially less #rain for Wed, Thur, and Fri.
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Articles
Normal vectors of a scalar field
This article gives the formula for the normal vectors of a surface defined by a scalar field on . The normal vector of the graph of the function at is . 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 , and then integrate the rest components.
- Categories: math
- Tags: calculus, vector analysis
It is Feb 29 today!
It is Feb 29 today. The date appears once for as long as 4 years!
- Categories: update
- Tags: fooling around
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).- Categories: programming
- Tags: ruby, meta programming, long paper
Amazing Siteleaf
I have been using Siteleaf to manage my blog. It is just convenient and amazing.
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.
- Categories: math
- Tags: linear algebra, long paper
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: . It turns out that we can write canonical equations , Poisson brackets , and canonical transformations in these complex numbers. Finally, I show two examples of using them in real problems: a free particle, and a harmonic oscillator.
- Categories: physics
- Tags: classical mechanics, canonical transformation, hamiltonian, complex, long paper
Giving birth to my own blog
This is my first blog! I will share interesting things in my life here.
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