Strictly Platonicteaching mathematics

through sculpture

Steven Zides Wofford College zidessb@wofford.edu

Why talk about Sculpture??

Sculpture: The art of making two- or three-dimensional representative or abstract forms, esp. by carving stone or wood or by casting metal or plaster.

Key Benefits:• Physical• Tactile• Ubiquitous• Personal

Anthropomorphic Representation“Classical Sculpture”

Michelangelo: Pieta The Townley Discobolus

Metaphoric Representation“Cubist/Futurist Sculpture”

Umberto Boccioni: Bottle in Space

Picasso: Head of a Woman

Platonic Representation“ Suprematist/Constructavist Sculpture”

Max Bill: Endless RibbonIvan Puni: Suprematist Relief-Sculpture

Morton C. Bradley Jr. (1912-2004)

• Attended Harvard in the late 1920’s

• Studied art collections in Europe in the mid - 1930’s

• A painting conservationist by profession

• Interests in linguistics, color theory, and musical composition

• Began creating algorithmic sculptures in the 1960’s

Morton C. Bradley Jr: Firebird “When Bradley took up making sculpture, he defined a language of vision with an abstract vocabulary of symmetrically forms and pure color, combined according to prescribed rules of repetition, reflection, and rotation.” --- Gamwell

Additional Works by Bradley

Morton C. Bradley Jr: Nautilus

Morton C. Bradley Jr: Regatta

Sculpture Related Activity I

This sculpture is the amalgamation of nested Platonic solids.

Instructions Get into your group and have the computer people research what it takes to be a Platonic solid. Also, how many of these solids exist and what do they look like? Now see if your group can determine which of the these solids occur in the sculpture.

Homework Read the article on Johannes Kepler. In what way was Kepler’s work influenced by the Platonic solids? Relate Kepler’s work back to the sculpture considered in class.

Morton C. Bradley Jr: Homage to Plato

Sculpture Related Activity II

This sculpture is a torus created by the twisting of a hypocycloid. The pattern on the bronze surface is known as Peano-Hilbert space filling curve.

Instructions Get into your group and have your computer people research the terms Mobius strip and hypocycloid. How is this sculpture similar and different from the Mobius strip? Using the Play-Doh provided, see if your group can create such an umbilic torus. If you ran your finger along the cusp (vertex) of the sculpture, how many times do you need to go around to get back to where you started? What shape would you need to twist if you wanted this number to be 5?

Helaman Ferguson: Umbilic Torus NC

Useful Resources

• Gamwell, Lynn. Color and Form. Bloomington: Indiana University Press, 2012

• Emmer, Michele. The Visual Mind II. Cambridge: MIT Press, 2005

• Peterson, Ivars. Fragments of Infinity. New York: John Wiley & Sons, 2001

• Ferguson, Helaman. Mathematics in Stone and Bronze. Erie: Meridian Creative Group, 1994

Strictly Platonicteaching mathematics

through sculpture

Steven Zides Wofford College zidessb@wofford.edu