Archive of posts with tag “long paper”
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
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