“In ancient times, music was considered a part of mathematics. Mathematics is the music of the mind; music is the mathematics of the soul.” Harald Ness, Jr. in “Mathematics; an Integral Part of Our Culture” in Humanistic Mathematics
An Infusion of the Fine Arts Barbra Steinhurst Pennsylvania College of Technology AMATYC 2007
Why Use the Fine Arts? • Students can relate • Fun for both teachers and students • Employ mathematics at both deep and superficial levels • Expand student notions of mathematics as a field
How to Design Activities • Use the art to motivate; extend the math • Use the art to illustrate; find the math • Use the art to teach the math explicitly • Use the art to assess understanding; students search out the math • Use the art to answer “when will I ever use this?”
Topics • Number Theoretic Ideas • LCM and Polyrhythms • GCF, relatively prime, Euclidean algorithm, and plaited mat sona • Functions
Polyrhythms • A polyrhythm is the co-occurrence of two or more rhythmic patterns. • Jazz syncopation • African and Indian drumming • Caribbean music • many others
Let’s Try It . represents a beat x represents a clap
Tschokwe sona • The sona are part of a rich storytelling tradition among the Tschokwe tribe in Africa. • Let’s Draw Some!
Topics • Number Theoretic Ideas • Functions • Inverse Functions and Lewis Carroll • Function Transformations and Bach
Hunting Snarks • Read the excerpt • Examine Stanza 8. What happens to the number three? • Suppose rather than the number 3, we use the variable x. Write a function f(x) that describes what operations occur in stanza 8.
Hunting Snarks • Examine Stanza 9. What is the input? • What happens to that input? • Write a function g(x) that describes the operations that occur in stanza 9.
Hunting Snarks • What is the relationship between f(x) and g(x)? (Hint: Find g(f(x)) and f(g(x)).) • How does that relationship tell us that the butcher will end with the number he starts with? • Did the Butcher show what he set out to show?
A Function Transformations Activitybased on The Art of Fugueby J.S. Bach
Set Up and Start Up • Define dependent and independent variables of this function • Translate musical notation into numerical function notation • Sketch the melodic contour of the function • Listen to the function
Lessons Learned • Warm students up to the idea • Careful demonstration • Did it bomb? Think quick and adapt. Don’t push it if not working. • The more you try it, the easier it gets.
Thank you! Barbra Steinhurst firstname.lastname@example.org http://www.musicandmath.com