Geometry: Patterns in Nature, Art, and the Cosmos

Universal Geometry: Patterns in Nature, Art, and the Cosmos
One-Time Class Outline (60 Minutes):
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Introduction (10 minutes)
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Ask students to share a natural or artistic pattern they find beautiful or intriguing (e.g., spirals in seashells, symmetry in snowflakes).

•	What is Universal Geometry?

Brief overview of how geometry connects patterns in nature, art, and science.
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Core Concepts (30 minutes)
1.	Patterns in Nature (10 minutes)

o	Explore the Fibonacci sequence and golden ratio using visuals like sunflowers, pinecones, and nautilus shells.

o	Discuss how these patterns appear naturally and mathematically.

o	Hands-On: Quick Fibonacci sequence calculation using a provided template.

2.	Fractals and Infinity (10 minutes)

o	Introduce fractals and their infinite self-similarity using examples.

o	Watch a short animated visualization of a fractal zoom.

o	Hands-On: Students create a simple fractal using a triangle or a branching tree diagram.

3.	Geometry in Art and Architecture (10 minutes)

o	Highlight the golden ratio and symmetry in famous works of art (e.g., Da Vinci’s Vitruvian Man) and architecture (e.g., Pyramids of Giza, Parthenon).

o	Discuss tessellations with examples.

o	Hands-On: Draw a simple tessellation or golden rectangle.
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Wrap-Up and Reflection (10 minutes)

•	Connection Discussion:
How does understanding geometry help us see the world differently?

•	Student Sharing:
Invite students to share what they found most fascinating or ask questions.