Patterns Across Space and Time

Fall Quarter Topics:

Patterns in Numbers:  Mathematical sequences including examples of periodic, arithmetic, geometric and other series in nature and art, in space and in time.  Explore the difference between mathematical proof and perceived patterns. 

Scale and Metamorphosis:  We will study how scaling laws limit the size and form of objects in nature and how it affects the shape of animals as they grow.  In this context we will also discuss how cartoon characters are often represented with childlike features (big round heads and eyes and shortened limbs)

Spiral Patterns:  We will study the Archimedes spiral, logarithmic spiral and other examples in art and nature.  There will be an extensive discussion of phyllotaxis – spiral pattern formation in plant growth and its connection with Fibonacci numbers. Other methods for spiral pattern formation will also be explored.

Symmetry:  What is symmetry? What is its role in math, science and art?  We will learn about groups of symmetries in rosette, frieze and wallpaper patterns.  We will draw on examples from other cultures (eg Islamic art, blanket patterns, pottery patterns and sand patterns).  We will also study the role of symmetry breaking in pattern formation in nature.

Winter Quarter Topics:

Fractals and Chaos:  We will examine what fractals are, how they are formed in nature and how they are represented in art. We will also study chaotic systems and model them using Mathemtica.

Cycles and Rhythms:  examples of cyclical motion in nature (eg tides, sunsets, circadian rhythms etc.)  We will also study the symmetry patterns of animal gaits.

Waves:  We will study create interference patterns with water waves and light. We will also visualize sound waves and their interference phenomena using Mathematica and SpectraFoo

Project work: Students will present independent work which synthesizes the topics from the two quarters