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Vortical Model of Philolaus' Cosmos

Vortical Model of Philolaus' Cosmos
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2019-08-06 23:32
FunctionTrigonometryCoordinate GeometryGraphing
This example demonstrates the graphical representation of Philolaus' vortical model of the universe. It involves core mathematical concepts such as functions, trigonometry, coordinate geometry, and transformations. The construction utilizes GeoGebra commands and objects like CurveCartesian for Cartesian curves, Rotate for rotation, and LaTeX for formatted text. Suitable for high school students and math enthusiasts studying cosmic models and mathematical expression.

GeoGebra Commands & Parameters

  1. CurveCartesian((θ; θ), θ, 0, (2 * 3.141592653589793)) → a
  2. CurveCartesian((θ; θ), θ, 0, (2 * 3.141592653589793)) → b
  3. Rotate((r, 0), Angle[θ + (((2 * π) * k) * t / r^(2))], aF) → cE
  4. LaTeX(t, true, true) → text2
  5. Rotate(((sqrt(4301.1) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(4301.1) * r))^(2))], aF) → iZ
  6. Rotate(((sqrt(10752.75) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(10752.75) * r))^(2))], aF) → jK
  7. Rotate(((sqrt(43011 / 71685) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(43011 / 71685) * r))^(2))], aF) → bC
  8. Rotate(((sqrt(43011 / 1458) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(29.5) * r))^(2))], aF) → dM
  9. Rotate(((sqrt(43011 / 486) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(88.5) * r))^(2))], aF) → eH
  10. Rotate(((sqrt(43011 / 118) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(364.5) * r))^(2))], aF) → gS
  11. Rotate(((sqrt(43011 / 62) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(693.73) * r))^(2))], aF) → hR
  12. Rotate(((sqrt(43011 / 180) * r), 0), Angle[θ + (((2 * π) * k) * t / ((sqrt(238.95) * r))^(2))], aF) → fA

AI Drawing Prompt Reference

Create a cosmic model based on circular motion, featuring multiple rotating circular paths with varying radii and angles. Start by drawing two circular paths, then rotate these paths around a central point using specific mathematical expressions for the radii and angles. Pay attention to the relationship between the rotation angle and the radius of each path.
The prompt above was compiled from the original drawing commands and is for reference only.