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// Spheres and Spirals in Dahlias, Alliums and Broccoli
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Classroom Contents
The Shape of Plants - Why Plants Love Mathematics and Mathematicians Love Plants
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- 1 // Intro – Why Plants Love Mathematics Fibonacci, Golden Ratio & Spirals
- 2 // Touring the Mathematical Garden: Polygons, Stars & Symmetric Plants
- 3 // Spheres and Spirals in Dahlias, Alliums and Broccoli
- 4 // Romanesco Broccoli: Self-Similar Spirals and Fractal Geometry
- 5 // What Is Phyllotaxis? Classifying Leaves, Flowers and Plant Organs
- 6 // Spiral Phyllotaxis in Sunflowers: Primordia, Heads and Hidden Geometry
- 7 // Counting Spirals: Parastichy Numbers and the Fibonacci Pattern
- 8 // Pine Cones, Pineapples & Succulents: Universal Fibonacci Spirals in Nature
- 9 // How Often Does Fibonacci Appear? Universality and the Divergence Angle
- 10 // Fibonacci Numbers Explained: Rabbits, Recurrence and Consecutive Ratios
- 11 // From Fibonacci Ratios to the Golden Ratio φ 1.618…
- 12 // Golden Rectangles, Divine Proportion and the Golden Angle 137.5°
- 13 // Continued Fractions, Kepler and the “Best” Approximation Property of φ
- 14 // Back to Plants: Shoot Apical Meristems, Fermat Spirals and Primordia
- 15 // Why the Golden Angle Packs Best: Irrational Slopes vs Rational Patterns
- 16 // How Plants “Compute”: Auxin Transport, Growth Mechanics and PDE Models
- 17 // Sherlock Holmes & Moriarty: Pascal’s Triangle, Fibonacci Codes and Plants
- 18 // Carnivorous Plants 101: Corpse Flower, Pitcher Plants and Morphology
- 19 // Modeling Pitcher-Plant Traps: Peristome Shape, Friction and Insect Dynamics
- 20 // Efficiency, Evolution and Trade-Offs in Carnivorous Plant Design
- 21 // Final Summary – Fibonacci, Golden Ratio and Why Mathematicians Love Plants
