Making-Scientific-Visualizations-with-the-Omniacs
🔄 Visualizing the Irrationality of Pi with Compound Rotations | Manim
This project uses Manim to illustrate the irrationality of π by animating two rotating vectors (arms) spinning at different rates. The resulting motion traces a non-repeating, beautifully tangled path.
🔢 What It Demonstrates
- Two arms rotate from a common origin:
- First rotates with angular velocity θ
- Second rotates faster by √4×θ (i.e., 2×θ)
- Red arm is anchored to the end of the yellow arm
- The tip of the red arm traces a complex, non-repeating path
- Duration of rotation: 60 seconds → full π motion cycles
🧠 Conceptual Significance
- The traced path never overlaps perfectly
- This illustrates incommensurable rotation periods
- Demonstrates π’s irrationality via visual geometry
🎨 Visual Features
| Element | Description |
|---|---|
| Yellow Line | Primary rotating vector (θ) |
| Red Line | Secondary rotating vector (2θ) |
| Blue Path | Traced tip of red vector |
| Smooth Motion | Controlled with ValueTracker |
| Frame Rate | 60 fps for fluid tracing |
📦 Requirements
- Python 3.8+
- Manim Community Edition
- NumPy
pip install manim numpy
▶️ How to Run
manim -pql Pi_Irrational.py compass2
Use -qh for high-resolution render. 📁 Files
Pi_Irrational.py — Animation script
README.md — This file
🎓 Ideal For
Teaching irrational numbers and π
Visual demonstrations of compound rotations
Math and physics education tools
Visual art in generative math
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