Your SlideShare is downloading. ×
0
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
2012 mooc lecture
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

2012 mooc lecture

531

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
531
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide
  • This is the crease pattern I showed earlier.
  • Transcript

    • 1. Mathematical methods in origami Robert J. Lang www.langorigami.com MOOC December, 2012
    • 2. Early (but not first)• Japanese newspaper from 1734: Crane, boat, table, “yakko- san”• By 1734, origami is already well-developed MOOC December, 2012
    • 3. Modern Origami• Akira Yoshizawa (1911- 2005)• Inspired a worldwide renaissance of origami MOOC December, 2012
    • 4. Origami Today• “Black Forest Cuckoo Clock,” (1987)• One sheet, no cuts MOOC December, 2012
    • 5. Klein Bottle MOOC December, 2012
    • 6. What Changed?Math!Two forms: “Origami Mathematics” number fields constructibility origami in higher dimensions, curved spaces QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. “Computational Origami” computability complexity algorithms for design and simulation MOOC December, 2012
    • 7. Basic Folds of OrigamiValley fold M u tain fo on ld MOOC December, 2012
    • 8. Crease Patterns QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. MOOC December, 2012
    • 9. Origami design• The fundamental equation:• given a desired subject, how do you fold a square to produce a representation of the subject? MOOC December, 2012
    • 10. Stag Beetle MOOC December, 2012
    • 11. A four-step processScu tbj e T r ee B as e M o de l e as y H a rd e as y MOOC December, 2012
    • 12. The hard step• How do you make a bunch of flaps? MOOC December, 2012
    • 13. How to make a flap MOOC December, 2012
    • 14. Limiting process• Skinnier flap leads to…• A (quarter) circle! MOOC December, 2012
    • 15. Other types of flap• Flaps can come from edges…• …and from the interior of the paper. MOOC December, 2012
    • 16. Unify• They’re all circles MOOC December, 2012
    • 17. Circle Packing• Many flaps: use many circles. MOOC December, 2012
    • 18. Creases• The lines between the centers of touching circles are always creases.• But there needs to be more. Fill in the polygons, but how? MOOC December, 2012
    • 19. Divide and conquer• The creases divide the square into distinct polygons that correspond to pieces of the stick figure. A E F B E F E F A A A B B A A E F 1 E F B B B B 1 1 C C C C 1 m.6 = 27 0 G H G H C C 1 1 G H D 1 G H A D D B C MOOC G H December, 2012 D
    • 20. Molecules• Crease patterns that collapse a polygon so that its edges form a stick figure are called “bun-shi,” or molecules (Meguro)• Different molecules are known from the origami literature.• Triangles have only one possible molecule. A a a E A A D a a D E b B B c b D b D c c C CB C b D c te bem l h at a ou “ b r lc r i ” ee MOOC December, 2012
    • 21. Quadrilateral molecules• There are two possible trees and several different molecules for a quadrilateral.• Beyond 4 sides, the possibilities grow rapidly. “-t r 4sa” “ a hr e s wos ” Hs i/ a a a i u imK ws k Me a a ak w Ln ag MOOC December, 2012
    • 22. Circles and Rivers• Pack circles, which represent all the body parts.• Fill in with molecular crease patterns.• Fold! MOOC December, 2012
    • 23. MOOCDecember, 2012
    • 24. Computer-Aided Origami Design• 16 circles (flaps)• 9 “rivers “ (connections) a tle (4 tin s e c sid ) n rs e ah e• 200 equations! e rs a ha ed nc ek bd oy tail fo le re g fo le re g h d le in g h d le in g MOOC December, 2012
    • 25. The crease pattern MOOC December, 2012
    • 26. Whitetail Deer MOOC December, 2012
    • 27. Mule DeerMule Deer MOOC December, 2012
    • 28. Roosevelt Elk MOOC December, 2012
    • 29. Bull Moose MOOC December, 2012
    • 30. Tarantula MOOC December, 2012
    • 31. Dragonfly MOOC December, 2012
    • 32. MOOCDecember, 2012
    • 33. Kabuto Mushi “Samurai December, 2012 Helmet” Beetle MOOC
    • 34. Eupatorus gracilicornis MOOC December, 2012
    • 35. Euthysanius BeetleRoosevelt Elk MOOC December, 2012
    • 36. Praying Mantis MOOC December, 2012
    • 37. Two PrayingMantises MOOC December, 2012
    • 38. Representational MOOC December, 2012
    • 39. Dancing Crane Dancing Crane MOOC December, 2012
    • 40. Barn Owl Barn Owl MOOC December, 2012
    • 41. Grizzly Bear MOOC December, 2012
    • 42. Tree Frog MOOC December, 2012
    • 43. Instrumentalists MOOC December, 2012
    • 44. Organist MOOC December, 2012
    • 45. Moving to 3D...• Mathematical descriptions have permitted the construction of elaborate geometrical objects from single-sheet folding: – Flat Tessellations (Fujimoto, Resch, Palmer, Bateman, Verrill) 3-D faceted tessellations (Fujimoto, Huffman) Curved surfaces (Huffman, Mosely) …and more! MOOC December, 2012
    • 46. Flanged sphere• Similar to concept demo’d by Palmer in 2000 (inspiration for this work) MOOC December, 2012
    • 47. MOOCDecember, 2012
    • 48. MOOCDecember, 2012
    • 49. MOOCDecember, 2012
    • 50. Mathematica Package MOOC December, 2012
    • 51. Applications in the Real WorldMathematical origami has found many applications in solving real- world technological problems, in: – Space exploration (telescopes, solar arrays, deployable antennas) – Automotive (air bag design) – Medicine (sterile wrappings, implants) – Consumer electronics (fold-up devices) – …and more. MOOC December, 2012
    • 52. Miura “map-fold”• A map of Venice with one degree of freedom MOOC December, 2012
    • 53. Miura-Ori, by Koryo Miura• First “origami in space”• Solar array, flew in 1995 MOOC December, 2012
    • 54. Umbrella MOOC December, 2012
    • 55. 5-meter prototype• The 5-meter prototype folds to about 1.5 meter. MOOC December, 2012
    • 56. Stents• Origami Stent graft developed by Zhong You (Oxford University) and Kaori Kuribayashi MOOC www.tulane.edu/~sbc2003/pdfdocs/0257.PDF December, 2012
    • 57. Folding DNA • Paul Rothemund at Caltech developed techniques to fold DNA into origami shapesPaul Rothemund, “Folding DNA to createnanoscale shapes and patterns,” Nature, 2006 MOOC December, 2012
    • 58. Origami5• Based on the 5th International Conference on Origami in Science, Mathematics, and Education (Singapore, 2010)• Next conference: Kobe, Japan, 2014 MOOC December, 2012
    • 59. Pots http://www.langorigami.com MOOC December, 2012

    ×