Skip to content

「Geometric Optics in Discrete Mathematics」- VS -「Wave Optics in Partial Differential Equations (PDEs)」

License

Notifications You must be signed in to change notification settings

ChenZhu-Xie/geometric_optics_2_discrete_mathematics

Repository files navigation

fig

An expedition ☛『Discrete Mathematics』in『Geometric Optics』

About

Description

  • 『This exploration process』is one of『the examples of the second book』
    • Using『Euclidean algorithm』to understand the『Multiple reflections』of light from the『Inner wall of the silver mirror』in the unsealed『Dewar bottle』
  • Discussed the application of algebra (mathematics) in geometry (optics)
    • External light source: when it enters the『pure reflection blackbody』from the outside, the light will eventually come out from the gap. Why?
    • Internal light source: when the source is inside the『pure reflection blackbody』,light may not necessarily come out from the gap. What are the corresponding conditions?

Inplementation

  1. Ideological perspective: Abstract the『optical process』in『concave mirror』into『mathematical process』
    • See the animation in file「Multiple Euclidean algorithm runs automatically in『Dewar bottle』=『pure-reflection non-absorbing notched blackbody』.pptx」
    • See the content『The origin of the circular vector』on page 8 of「2.『Illusions_of_Illustrations_·_Zodiac』.pdf」
  2. Optical Expansion:『Integral Sphere with Notches』➞『Maze with Exits』
    • The same conclusion applies to『any other shape』, such as a『labyrinth-shaped cavity』
    • That is to say, the shape of a blackbody may not necessarily be spherical
      • If the light source is『inside the maze』, the light『may not be able to solve/escape the maze』
      • See the case『Maze solution
      • If the light source is『outside the maze』, then the light『can definitely come out of the maze again』
      • fig
      • fig
  3. Mathematical Expansion:『Bivariate』to『Multivariate』linear indeterminate equation ('s Special/General solution)

History

About

「Geometric Optics in Discrete Mathematics」- VS -「Wave Optics in Partial Differential Equations (PDEs)」

Topics

Resources

License

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published

Languages