Phi 1.61803: Art in Math and Science   Western Reserve Public Media

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:

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:


Chuck Close

Ratio, Proportion and Percent

Chances are good that when your students think of beauty and objects that are most pleasing to the eye, they aren’t thinking of ratio, proportion or percent. But this unit, which is inspired by the work of artist Chuck Close, might change that.

Comfort with these mathematical concepts gives any person a better way of seeing the world around him. With mathematical eyes and a solid knowledge of ratio, students will grow up to be better consumers. For that reason, understanding ratio, proportion and percentage is a valuable concept to teach.

The unit begins with several PowerPoint presentations that introduce the concepts of ratio, unit rate and proportion to your classes. These presentations are supported with various activities and handouts that ask students to solve puzzles using their new knowledge. Your classes move on to the Fibonacci sequence and the golden ratio. They apply these concepts to Chuck Close’s artwork as it was displayed at the Akron Art Museum. The final project asks students to use the same process on a picture of themselves or someone they know.


Standards Addressed
Grade 5 , Mathematics — Number, Number Sense and Operations Standard

05-07 Benchmark D. Use models and pictures to relate concepts of ratio, proportion and percent.

Y2003.CMA.S01.G05-07.BD.L05.I01 / Number and Number Systems

01. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.



Pattern ID

Interior Angles of Triangles and Quadrilaterals

Our diverse buildings, diamond jewelry, traffic patterns, modern art, classical furniture, Broadway stage designs and simple tools of daily living are all constructed of angles. Understanding angles increases both artistic appreciation and comprehension of function.

This unit begins with a PowerPoint lesson that leads students through the basics of angles and the use of protractors. They test their knowledge using puzzles and apply that specific learning to quadrilaterals.

The final project for this unit requires students to build their own octahedrons. Directions for the project are specific and give your students a chance to use their new knowledge of angles. Students make the finished octahedron into a fun predicting toy similar to the classic Magic Eight Ball toy.


Standards Addressed
Grade 5, Mathematics — Geometry

05-07 Benchmark D. Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

Y2003.CMA.S03.G05-07.BD.L05.I05 / Characteristics and Properties

05. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals.



Mark Mothersbaugh

Sound Energy

Controlling sound is important to health, mood, entertainment and especially communication. Mark Mothersbaugh, an original member of the rock band Devo and an Ohio native whose work has been featured at the Akron Art Museum, was the inspiration for this unit. Both he and the museum are interested in the art of sound. A beginning understanding of the basics about the transmission, reflection and absorption of sound waves would be useful to anyone. This unit is designed to support and focus your lessons.

The unit begins by asking students to explore sound in various ways to solidify understanding that it is caused by vibration. Students are then introduced to the families of sound found in a modern orchestra. They also get to know Mark Mothersbaugh through an interview in which he discusses sound and what it has meant to him. Your classes finalize their learning with a project that requires them to design and build their own instrument. They must be able to use it to explain and demonstrate both volume and pitch.


Standards Addressed
Grade 5, Science — Physical Science

3-5 Benchmark F. Describe the properties of light and sound energy.

Y2003.CSC.S03.G03-05.BF.L05.I06 / Nature of Energy

06. Describe and summarize observations of the transmission, reflection and absorption of sound.

Y2003.CSC.S03.G03-05.BF.L05.I07 / Nature of Energy

07. Describe that changing the rate of vibration can vary the pitch of a sound.




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


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

Executive Producer
Maria Mastromatteo, Western Reserve Public Media

Duilio Mariola, Western Reserve Public Media

Duilio Mariola, Western Reserve Public Media

Student Script
Larry Chance, Chance Productions

Teacher Script
Cathy Adler, Ravenna City School District


Layout and Design
Paula Kritz, Western Reserve Public Media


This series was funded by the Ohio Legislature through the eTech Ohio Commission. Copyright©2010, Northeastern Educational Television of Ohio, Inc. All rights reserved.
Overview Ratio, Proportion and Percent Interior Angles Teacher Materials Sound Energy Online Resources Watch Online