Educational activities related to Piano-Hinged Dissections: Time to Fold!

Student activities based on the book

Lycée Fauriel, Saint-Etienne, France
September 2004: Daniel Goffinet, who teaches mathematics at the Lycée Fauriel, in Saint-Etienne, France, wrote to me in the summer of 2004. He had seen my folding-box article in the College Mathematics Journal, based on my section, "Folderol 1: A New Wrinkle for an Old Folding Problem." He enjoyed the article and decided to make a problem of it for his calculus students when they returned in September. He observed that I could have said more about the conditions under which the volume achieves a maximum. (He was right, though I actually said more in the journal article than in the Folderol section!) One needs to take into account the physical limits of the box design, as well as the function to be maximized, when determining the domain over which we are optimizing.

In September, Daniel reported to me:
"I have finished reading the papers about your box-volume (I had added questions about the A4 paper size and the construction of the lengths that arise in the formulas)

It proved to be a very good divider among those students : - about half of them were aware of the domains problems, some solved it with A4 size or a square ... some of them went all the way to study the case of "any a and b" - about half of them were unaware of the domains problems ... they merely computed derivatives, plugged some numbers in the formulas, quite blindly ... I got 5 or 10 volumes measured in square meters."
I hope that all the students had a good time with this somewhat different folding problem!
Harvard University Graduate Scool of Design: GSD1101, Introduction to Design and Visual Studies in Architecture, Fall 2013
Inaki Abalos, Katy Barkan, Jeffry Burchard, Kiel Moe, Megan Panzano, Ingeborg Rocker, Cameron Wu chose as their project 3 in the Harvard Graduate School course 1101 a project involving piano-hinged dissection as exemplified in Chapter 12: "From Fifi to Zulu and Back".
"The technique of hinged polyhedral dissection (3-D only, not 2-D) will serve as a geometric armature which will regulate spatial relationships between the two architectural proposals. You are NOT designing a singular kinetic building solution capable of adaptation. Rather, you must propose two distinct yet related organizations. The hinged dissection’s particular characteristic of physical transformation whereby interior surfaces/volumes become exterior and vice versa is compatible with the requirement to propose opposing strategies of thermodynamic configuration. It imbricates the two proposals in a coherent geometric logic while simultaneously producing remarkable spatial variations which may facilitate the elaboration of other related architectural ideas."
Don't ask me what this means. I'm not an architect!

Last updated June 13, 2014.