Dr. Beardicus' Theorem

A Computational Study on the Correlation Between Anime Profile Pictures, Beard Prominence, and Medieval Fantasy Dwarf Probability

Overview

This repository contains the implementation and documentation of Dr. Beardicus' Theorem, a groundbreaking mathematical framework that explores the unexpected relationships between anime profile pictures, facial hair growth, and Medieval Fantasy Dwarf tendencies in online communities.

Key Findings

• Users with cuter anime profile pictures tend to have more prominent beards
• Beyond a critical cuteness threshold (A = 8), users show increasing probability of being Medieval Fantasy Dwarfs
• The relationships follow precise mathematical formulas, enabling accurate predictions

The Theorem

Dr. Beardicus' Theorem establishes two fundamental relationships:

Beard Prominence (B)

$$ B = \frac{A^2}{10} $$ where:

• $B$ = Beard prominence score (0-10)
• $A$ = Cuteness level of anime profile picture (0-10)

Medieval Fantasy Dwarf Probability (P)

$$ P = \frac{1}{1 + e^{-(A - 8)}} $$ where:

• $P$ = Probability of being a Medieval Fantasy Dwarf (0-1)
• $A$ = Cuteness level of anime profile picture (0-10)

Visualizations

1. Beard Prominence vs. Cuteness Level

The quadratic relationship shows accelerating beard growth with increasing cuteness

2. Medieval Fantasy Dwarf Probability vs. Cuteness Level

A sigmoid curve demonstrating the sharp transition in Medieval Fantasy Dwarf probability around A = 8

3. Combined Analysis

Dual-axis visualization showing the interplay between beard prominence and Medieval Fantasy Dwarf probability

Repository Structure

.
├── README.md           # This documentation
├── Story.md           # The narrative behind the theorem
├── Theorem.md         # Formal mathematical definitions
├── beardicus_theorem.py # Interactive visualization app
└── screenshots/       # Example visualizations
    ├── 1.png         # Beard Prominence plot
    ├── 2.png         # Medieval Fantasy Dwarf Probability plot
    ├── 3.png         # Combined analysis
    └── theyhavebeards.jpg # Supporting evidence

Getting Started

Prerequisites

• Python 3.6+
• pip package manager

Installation

1. Clone the repository:

   git clone https://github.com/HxHippy/Beardicus-Theorem.git
   cd Beardicus-Theorem

2. Install dependencies:

   pip install -r requirements.txt

Running the Application

Launch the interactive visualization:

streamlit run beardicus_theorem.py

Implementation Details

Data Generation

• Cuteness level ($A$) sampled from [0, 10] in 0.1 increments
• Beard prominence ($B$) calculated using quadratic formula
• Medieval Fantasy Dwarf probability ($P$) computed using sigmoid function

Tools Used

• NumPy: Numerical computations
• Matplotlib: Static plotting
• Streamlit: Interactive web interface

Results

Key Observations

1. Beard Growth Pattern

   • Minimal growth for $A < 3$
   • Moderate growth for $3 ≤ A ≤ 7$
   • Rapid growth for $A > 7$

2. Medieval Fantasy Dwarf Transformation

   • Low probability ($P < 0.1$) for $A < 6$
   • Critical threshold at $A = 8$ ($P = 0.5$)
   • High probability ($P > 0.7$) for $A > 9$ of being a Medieval Fantasy Dwarf

Future Work

Potential Extensions

• Real-world data collection and validation
• Machine learning for cuteness assessment
• Beard density analysis using computer vision
• Cross-cultural Medieval Fantasy Dwarf identification patterns

Known Limitations

• Simulated data only
• Simplified beard growth model
• Cultural bias in Medieval Fantasy Dwarf classification

License

This project is licensed under the MIT License - see LICENSE for details.

Acknowledgments

• Dr. Beardicus for the original theorem
• The open-source community
• All the bearded Medieval Fantasy Dwarfs who inspired this work

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This is a work of mathematical whimsy. Any resemblance to actual beards or Medieval Fantasy Dwarfs, living or legendary, is purely coincidental.