Phi 1.61803: Art in Math and Science

Three lessons included in this guide relate the mathematical concept of phi to the beauty of art. The lessons include formative and summative assessments, teacher resource pages, student handouts, a professional development video and more. A companion music video that resembles “Schoolhouse Rock” studies artwork that was exhibited at the Akron Art Museum to help students understand the concept.

Phi (Φ) is a Greek symbol that stands for 1.61803. This number is derived from the golden ratio and has been studied for many years — from Pythagoras and Euclid to the astronomer Kepler to the present-day physicist Roger Penrose. Phi appears in the proportions of human and animal bodies, in plants, in DNA, in the solar system, in art and architecture, in music, in population growth, in the stock market and in theology. It is believed that the golden ratio is considered the divine proportion and illustrates the concept of beauty. Source: http://www.goldennumber.net/neophite.htm.

Let’s look at one way the golden ratio can be derived. During the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for phi. If you start with zero and one, each new number in the series is simply the sum of the two numbers before it. The series looks like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …

The ratio of each successive pair of numbers in the series approximates phi (1.61803…) because five divided by three is 1.666… and eight divided by five is 1.60. After the 40th division, the number is accurate to 15 decimal places. Source: http://www.goldennumber.net/fibonser.htm.

Credits

Project Coordinator
Maria Mastromatteo, Western Reserve Public Media

Teacher Guide
Teacher Design Team
Cathy Adler, Ravenna City School District

Christi Bates, Kent City School District

Maria Mastromatteo, Western Reserve Public Media

Teacher Guide Layout and Design
Paula Kritz, Western Reserve Public Media

Video
Produced by Western Reserve Public Media (WNEO/WEAO, Youngstown/Akron, Ohio)

Executive Producer
Maria Mastromatteo, Western Reserve Public Media

Producer
Duilio Mariola, Western Reserve Public Media

Videographer
Duilio Mariola, Western Reserve Public Media

Student Script
Larry Chance, Chance Productions

Teacher Script
Cathy Adler, Ravenna City School District

Web
Layout and Design
Paula Kritz, Western Reserve Public Media

Funding
This series was funded by the Ohio Legislature through the eTech Ohio Commission.