Knapp Week At USD

With the Demaines!

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About Knapp Week (April 16th - 23rd, 2018)

We welcome Professors Erik and Martin Demaine from MIT as the spring 2018 Knapp Chairs at the University of San Diego! As part of their visit we invite the San Diego and Tijuana communities to engage in creative, playful, interdisciplinary thinking with the Demaines, a cross-national collaboration that will result in the development of new works infused by the rich assets of our diverse communities. During the week of April 16-23, 2018, several creation stations will run in parallel (see below). Participants of all ages at the different sites will simultaneously create based on challenges inspired by the work of the Demaines. The explorations at these stations will be streamed to the Humanities Center at USD throughout the week. Some of the collaborative art will be "folded" into an exhibit that will include work by the Demaines, "Folding Borders, Making Unfoldings" in time for the gallery opening reception on April 27.

The Knapp Chair of Liberal Arts was established in 1995 by a generous endowment from the estate of Mary and Churchill Knapp of La Jolla, California, long-time supporters of the College of Arts and Sciences at the University of San Diego. The Knapp Chairs contribute to the vitality and centrality of liberal arts in the College by teaching and interacting with students, collaborating with faculty, and presenting public lectures that engage our campus community in confronting humanity’s urgent challenges.

We invite you to explore with us and join in our cross-national collaboration by sharing a picture of your work. Check back for exploration instructions starting on April 16th, 2018 and submit a picture of your work (see below).

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Copyright Erik and Martin Demaine

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Copyright Erik and Martin Demaine

Erik Demaine

Erik Demaine is a Professor in Computer Science at the Massachusetts Institute of Technology. Erik's research interests range throughout algorithms, from data structures for improving web searches to the geometry of understanding how proteins fold to the computational difficulty of playing games. He received a MacArthur Fellowship as a “computational geometer tackling and solving difficult problems related to folding and bending—moving readily between the theoretical and the playful, with a keen eye to revealing the former in the latter." He appears in the origami documentaries "Between the Folds" and NOVA's "The Origami Revolution." Erik's Website.
Click here to read more about The Genius Who Plays For a Living.

Martin Demaine

Martin Demaine, an artist and mathematician, is the Angelika and Barton Weller Artist in residence at MIT. After studying glassblowing in England, he started the first private hot glass studio in Canada and has been called the "father of Canadian glass." Martin's pieces from this period are represented in the permanent collections of major museums including the Canadian Museum of Civilization and the National Gallery of Canada. He is a Research Associate of the Mathematics Department at USD. Martin's Website.



As a father/son duo, Martin and Erik use their exploration in sculpture to help visualize and understand unsolved problems in science, and their scientific abilities to inspire new art forms. Their work includes curved-crease sculptures in the permanent collections of the Museum of Modern Art in New York, and the Renwick Gallery in the Smithsonian. They won a Guggenheim Fellowship (2013) for exploring folding of other materials, such as hot glass.



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Copyright Erik and Martin Demaine.

How can you join the fun?
  1. Come to one of the lectures at USD (dates and times below) or through the live stream below.
  2. Play, explore, and create at one of the creation stations at USD or in the San Diego and Tijuana communities. View stations here.
  3. Enjoy the exhibit at the USD Humanities Center (details below).
  4. Follow the instructions below to begin your own exploration and become part of our cross-national collaboration by sharing a picture of your work.
Click to share pictures of your work.
Challenges

Martin and Erik love to play! We invite you to join them! Each challenge begins with a list of materials and initial steps to gain familiarity with an idea. Suggestions are then provided to inspire your self-directed exploration which can lead to new creations. The challenge concludes with a list of additional resources. Choose one or more challenges or combine them to play, explore, create and share! Remember that making mistake is part of the learning process, so embrace them and have fun!

New Challenges will be released daily, stay tuned!

CHALLENGE #1: CREASE PATTERN ART


MATERIALS

To get started: A piece of paper (it could be a square, a rectangle or another shape).
To explore (suggestions): crayons, markers, colored pencils, watercolors, pieces of paper of different types.


INITIATION

Step 1: Fold the piece of paper. You could make something you know how to fold (a cootie catcher, a boat, an airplane, a sonobe module, a crane, etc.), something you find online, or fold to your heart’s content.
Step 2: Unfold the piece of paper and examine the crease pattern.


EXPLORATION-CREATION

Step 2: Get your creative juices flowing and come up with your own creations by making variations.

Step 3: Get your creative juices flowing and come up with your own creations by coloring the crease patterns. Some possibilities:

  • Color in an abstract way.
  • Aim to make the result look like something. For example, might it be possible to create a crane, and color in an elephant within the crease pattern.
  • Try to color it using the smallest number of colors such that no two adjacent regions have the same color.
  • Highlighting geometric shapes.
  • Something else that peaks your interest.

Step 4: Consider what you might be curious about. For example, what's the smallest number of colors needed to ensure that there is a way to color any map such that no two adjacent regions have the same color. Or what is the polygon with the largest number of sides in your crease pattern? What’s the relationship between each fold and the crease pattern it makes? What other questions do you have?


ADDITIONAL RESOURCES

Martin and Erik have collaborated with hundreds of people. They believe that, “It's a lot of fun to work with lots of people...You can solve bigger problems when you work with people who know different things.” One of their collaborators is Robert Lang, another world leading master of origami. Here is a link to information from Robert Lang about Crease Patterns as Art: Crease Patterns as Art.

CHALLENGE #2: EXPLORE AND CREATE WITH PLEATED HYPARS


MATERIALS

To get started: A square piece of paper.
To explore (suggestions): pieces of paper of different types, sheets of other materials, small binder clips or paper clips and/or other adhesive materials.


INITIATION

Step 1: Start with a square piece of paper and build a Pleated Hypar (Hyperbolic Paraboloid).

  • Erik Demaine shows the folding process from 1:44:53 to 1:54:06 of this video of Erik Demaine (Click Me), (December 7, 2015).
  • And/or follow the written and visual instructions:
    Folding Instructions
  • And/or print this crease pattern on a piece of paper and fold along the lines of the crease pattern (fold the darker lines in one direction--mountain folds, and then turn the piece of paper over to fold the lighter lines in the other direction):
    Folding Instructions

Note: If you make a crease that is longer than what’s shown in the crease pattern, don’t worry. Keep following the instructions and you should still get a pleated hypar.
Step 2: The pleated hyperbolic paraboloid models date back to a course on paper study taught at the German Art School Bauhaus by Josef Albers in 1927–1928. The Demaines became interested in this model about 19 years ago and have made thousands of them. This model began an exploration from art to mathematics to art to mathematics, etc., that led to their curved crease art, now in the permanent collection of the Museum of Modern Art in New York, and the Renwick Gallery in the Smithsonian. Check out more information about hyperbolic paraboloids and about some of the hypar explorations of the Demaines:

  • A video description of the pleat folding explorations of the Demaines for the previous 11 years, from Art to Math to Art to Math…, from 10:56 to 20:00 of Demaine folding exploarations (EG4 Conference, 2010).


EXPLORATION-CREATION

Step 3: Get your creative juices flowing and come up with your own creations based on the pleated hypar by doing any one or combination of the following:

  • Varying the instructions of the pleated hypar to create a new object by changing the size of the sheet, the angles of the folds, the distance between folds, the shape of the sheet, the percentage of paper that is folded, the materials used, or some other aspect.
  • Assembling several hypars to create a new object. You could initially use binder clips or paper clips to hold two hypars together as you explore.
  • Another idea you have.

Step 4: Consider what you might be curious about.


ADDITIONAL RESOURCES

To learn more:

Some examples of hyperbolic paraboloids in the world:

CHALLENGE #3: CURVED CREASES


MATERIALS

To get started: A piece of paper, a sturdy circular plate, something with a sharp point (pen, pencil, compass, small metal skewer, paperclips, screwdriver), tape (if you want).
To explore (suggestions): pieces of paper of different types, plates of different sizes.


INITIATION

Step 1: Practice making curved creases. If this is the first time you’re making curved creases, consider using a piece of paper that is smaller than the plate. Parts of circles/open curves are easier to fold than whole circles/closed curves.

  • Place the sheet of paper on a piece of cardboard to protect the surface below and allow for the creases to form. If you need help keeping the paper steady on the cardboard, consider securing the paper to the cardboard with a piece of tape.
  • Place a plate on the paper so that part of the circumference of the plate is on the paper.
  • Score the paper along the edge of the plate (as if you were drawing that part of the circle on the paper) with the metal point of the compass (or other sharp object). Make sure you score with enough force to make a sharp crease, but without damaging the paper (that comes from practice). Then move the plate to other parts of the paper and repeat this process a few times until you have several parts of circles scored. You can turn the paper upside down to score some of the circles that way.
  • Fold along the curves. You could fold these sections in an alternating pattern: a “valley” fold, a “mountain” fold, “valley,” “mountain,” etc.

EXPLORATION-CREATION

Step 2: Get your creative juices flowing and come up with your own creations by making variations.

Step 3: Consider what you might be curious about. For example, what happens when the circles intersect each other?


ADDITIONAL RESOURCES

CHALLENGE #4: PLEATED VASES


MATERIALS

To get started: A rectangular piece of paper.
To explore (suggestions): pieces of paper of different types, sheets of other materials, small binder clips or paper clips and/or other adhesive materials.


INITIATION

Step 1: Fold the piece of paper accordion style, so that the creases are parallel to the shorter side of the paper. Remember to make sharp creases.
Folding Instructions
Step 2: Close the accordion. Take either end of it and fold it. Make sure that the creases are sharp. Make observations about the crease pattern.
Step 3: Unfold the paper and look carefully at the crease pattern. All of your “v” creases will need to be in the same direction (see red creases below). Thus, make all of them “mountain” or all of them “valley”.
Step 4: As you encounter the long creases (the ones that are as long as the long side of the paper), change their direction once they pass through the “v” creases. The purple parts should all be mountain folds and the blue parts should all be valley folds.
Step 5: Continue to change the direction of your folds, as needed, until you’ve reached the end of your paper.

Step 6: Attach the two shortest sides of your paper to each other with a gluestick, paperclips, etc., to create your object.

If the pleated paper is not long enough, consider making one that is longer, or making another one of the same size to attach to yours.


EXPLORATION-CREATION

Step 7: Get your creative juices flowing and come up with your own creations based on the pleated vase.

Step 8: Consider what you might be curious about.

ADDITIONAL RESOURCES

Instructions for the pleated vases:

CHALLENGE #5: Strip Folding


MATERIALS

To get started: A long strip of thin paper.
To explore (suggestions): a roll of paper, tape, a ruler, a computer or phone (to look up the strip folding font of the Demaines).


INITIATION

Step 1: Fold the the strip of paper to create the first letter of your name or something else you want.


EXPLORATION-CREATION

Step 2: Erik and Martin Demaine have created several fonts and puzzle fonts inspired by mathematical problems that were not yet solved, puzzles, etc. Take a look at several examples of fonts created by the Demaines and others: Oragami Fonts By Erik Demaine.

Step 3: Go to this link and write a short word in the “enter text to render box.” Using a ruler, mark the squares needed on a roll of paper to create that word, as shown on the crease pattern below the box. Follow the given crease patterns to create your word. Use tape along the way so the letters don’t become undone.

Step 4: Get your creative juices flowing and come up with your own folding strip creations.

Step 5: Inspired by the fonts of the Demaines, think about a font you may want to create that involves folding.

Step 6: Consider what you might be curious about.

ADDITIONAL RESOURCES

To learn more:

CHALLENGE #6: FOLD-AND-ONE-CUT


MATERIALS

To get started: Paper, print-outs of Demaine example designs to fold-and-cut (print examples from here: Click here), scissors.
To explore (suggestions): pieces of paper of different types, scissors, computer (to explore more information online).


INITIATION

Step 1: Start with a printed example from the fold-and-cut website (Fold cut examples).
Try to fold your shape and cut along just one straight line to produce the shape outlined with the solid lines.

Harry Houdini used to perform a trick where he would fold a piece of paper several times, make one straight cut, and would create surprising results. The Demaines proved that any shape made up of straight sides can be created in this way. Watch Erik Demaine talk about the one-cut problem.

  • A video description of the one-cut problem from 2:20 to 6:38 of May 2, 2011 Math Encounters - The Geometry of Origami, National Museum of Mathematics, MoMath: Video Description.

EXPLORATION-CREATION

Step 3: Get your creative juices flowing and come up with your own creations based on the one-cut problem.
Draw a shape made up of line segments, and try to cut it out using some folding and just one cut.

  • Explore the fold-and-cut font that Martin and Erik created: Simple fold cut.
  • Create your own fold-and-cut font.

Step 4: Consider what you might be curious about.

ADDITIONAL RESOURCES

To learn more:

  • Check out the history and mathematics of the fold-and-cut problem at: Fold cut.
  • Erik Demaine’s Lecture at MIT on the one-cut problem: MIT Lecture.

Some articles that introduce examples where the one-cut problem was useful:

CHALLENGE #7: POP-UP CARDS


MATERIALS

To get started: Paper, scissors, hobby knife, a piece of thick cardboard to cut on.
To explore (suggestions): pieces of paper of different types, scissors, hobby knife, computer (to explore more information online).


INITIATION

Step 1: Fold the piece of paper in half and use scissors or a hobby knife to make cut a few curves (or lines) on the paper. Practice reverse-folding some of the parts between cuts. Here are some video instructions:
Easier: Video Instructions
Complex: Video instructions.


EXPLORATION-CREATION

Step 2: Get your creative juices flowing and come up with your own pop-up cardboard models or Create Murphy furniture.

Step 3: Go to this link and write a short word in the “enter text to render box.” Using a ruler, mark the squares needed on a roll of paper to create that word, as shown on the crease pattern below the box. Follow the given crease patterns to create your word. Use tape along the way so the letters don’t become undone.

Step 4: Consider what you might be curious about.

ADDITIONAL RESOURCES

To learn more and get inspiration:

CHALLENGE #8: FOLD-A-CUBE


MATERIALS

To get started: Paper (a 3 by 3 grid of squares), scissors, hobby knife.
To explore (suggestions): Paper, scissors, hobby knife, coloring pencils, markers.


INITIATION

The Demaines LOVE puzzles! Folding Instructions


Step 1: Start with a 3x3 grid of squares. The puzzle consists of creating a cube using the grid of squares.

  • Make slits along the sides of some of the small squares (the whole side) so that you are able to arrange the squares to create a cube.
  • Note that some of the squares will need to overlap.
  • Make sure you don’t cut off any of the squares completely.
  • Once you find a solution, decorate your cube so that you know where each square belongs and which are its neighboring squares.
  • Open up your cube and try to put it back together.

EXPLORATION-CREATION

Step 2: Get your creative juices flowing:

  • Can you find other solutions? How many solutions are there? How can you be sure there are no more?
  • What happens if you change something about this puzzle? What happens with more squares? Fewer squares? What if you have triangles instead? What can you build? What would be a good puzzle with triangles? Pentagons? Other shapes? Other possibilities?

Step 3: Consider what you might be curious about.

ADDITIONAL RESOURCES

To learn more and get inspiration:
Martin and Erik say: “We love puzzles. When Erik was six years old, we designed and made puzzles as the Erik and Dad Puzzle Company. Now we do research on combinatorial games and puzzles, in particular analyzing the computational complexity of games and puzzles we like to play.”
Check out some Puzzles (Click Me).

CHALLENGE #9: DEMAINE PAPER PUZZLES


MATERIALS

To get started: Print out: PCOC2005 puzzle. (or black and white squares)
To explore (suggestions): Paper, coloring pencils, markers.


INITIATION

Erik and Martin Demaine sometimes create special puzzles to celebrate special events and milestones. We will explore some of those puzzles here.


Step 1: Explore and solve one of the puzzles:

  • Print out: Black and White puzzles (see PCOC2005 puzzle for more information)
  • Cut out the 4x4 color pattern square in the top left
  • Fold along some of the indicated creases to make a 2x2 square that’s grey on both sides.
  • Or, fold along some of the indicated creases to make a 2x2 square that’s grey on one side and white on the other side. This is harder!

EXPLORATION-CREATION

Print and solve other puzzles created by the Demaines:

Step 2: For more information and variations, see:

Create your own folding puzzle! Just follow these steps:

  • Fold a piece of paper flat, however you want. (This will be the solution!)

  • Draw some imagery, text, or anything identifiable as the solution.

  • Unfold, and redraw onto a fresh piece of paper to hide the creases.

  • (Optionally) draw some extra distractions in the remaining blank space.

Step 3: Consider what you might be curious about.

ADDITIONAL RESOURCES

To learn more and get inspiration:


Martin and Erik say: “We love puzzles. When Erik was six years old, we designed and made puzzles as the Erik and Dad Puzzle Company. Now we do research on games and puzzles, in particular analyzing the computational complexity of games and puzzles we like to play.” Check out some puzzles! (Click me).

Event Details
Knapp Lecture: PLAYING WITH ART AND SCIENCE: ORIGAMI, GLASS, AND MATHEMATICS

Time: Monday, April 16, 2018, 6:00 p.m.

Location: Joan B. Kroc Institute for Peace and Justice Theatre


Father/son duo Martin and Erik Demaine like to blur the lines between art and mathematics, by freely moving from designing sculpture to proving theorems and back again. Paper folding is a great setting for this approach, as it mixes a rich geometric structure with a beautiful art form. Mathematically, they are continually developing algorithms to fold paper into any desired shape. Sculpturally, the duo has been exploring curved creases, which remain poorly understood mathematically, but have potential applications in robotics, deployable structures, manufacturing, and self-assembly. By integrating science and art, they constantly find new inspirations, problems, and ideas: proving that sculptures do or don’t exist, or illustrating mathematical beauty through physical beauty. Collaboration, particularly as a father-son team, has been a powerful way for them to bridge art and mathematics. Prior to the lecture, guests will be able to view a sneak peek of the exhibition in the Humanities Center Gallery starting at 4 p.m.

Knapp Conversation: BUILDING with MATHEMATICS, ART, and COMMUNITY at USD

Time: Thursday, April 19, 2018, 7:00 p.m.

Location: Humanities Center,
Serra Hall 200
(Max Capacity: 40 people)


Father/son duo Martin and Erik Demaine explore the worlds of sculpture, manufacturing, and shape based on the notion of scale. In particular, they explore ideas behind several parallel creation stations (including two located at USD, one in Linda Vista, one in Tijuana) that allow participants to simultaneously create based on certain rules inspired by the work of Martin and Erik. Some of these creations will be "folded" into the exhibit, "Folding Borders, Making Unfoldings" prior to the gallery opening reception on April 27.

Gallery Exhibition: Folding Borders, Making Unfoldings

Time: Monday, April 16, to Friday, May 18, 2018

Location: Humanities Center Gallery, Serra Hall 200


Folding Borders, Making Unfoldings will feature work by the Demaines and work created in several parallel creation stations — including two located at USD, one in Linda Vista and one in Tijuana — that will allow participants to simultaneously and spontaneously create based on certain rules inspired by the work of Martin and Erik. The exhibit will begin with a few pieces by the Demaines and the collaborative creations will be “folded” into the exhibit prior to the gallery opening reception.

Exploration Stations
All USD Campus San Diego Area Tijuana
Words from the Demaines
Thank you

These events are possible through support from the University of San Diego Knapp Chair of the Liberal Arts, Humanities Center, Fletcher Jones Foundation, College of Arts and Sciences and Shiley-Marcos School of Engineering; the Dolciani Fund of the Mathematical Association of America; our community partners: High Tech High, Escuela Libre de Arquitectura, Advancing Students Forward and Chula Vista Library; and the Massachusetts Institute of Technology.