| [+] Hinged dissections: Locked and unlocked chains of planar shapes, adorned chains, slender adornments, slender implies not locked, Kirszbaun's Theorem, locked triangles with apex angle > 90°; existence of hinged dissections, refinement. | ||||
| This lecture is about chains of polygons, or other 2D shapes, connected together by hinges in 2D. These structures are classically called “hinged dissections”. On the foldability side, we'll see some surprisingly general situations, called “slender adornments”, where these chains cannot lock, building on the Carpenter's Rule Theorem and expansiveness (Lecture 11). We'll also see some examples that do lock, building on our theory of infinitesimally locked linkages and Rules 1 and 2 (Lecture 12). On the design side, we'll show that we can actually design hinged dissections that fold into any finite collection of desired polygonal shapes, using slender adornments to guarantee foldable motions. | ||||
We will have a guest lecture by Benjamin Parker, one of my favorite artists in the world of origami tessellations. You can see some of his work on his website, http://www.brdparker.com/. Then we'll work on problems related to polyhedron unfolding. |
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Handwritten notes, page 1/8 •
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Slides, page 1/14 •
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Figure 1 of http://erikdemaine.org/papers/LockedShapes_DCG/ (covered under the MIT Faculty Open-Access Policy) Slides, page 1/14 • [previous page] • [next page] • [PDF] |
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