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Geometric constraint solving
 Computing in Euclidean Geometry
, 1995
"... We survey the current state of the art in geometric constraint solving. Both 2D and 3D constraint solving is considered, and different approaches are characterized. ..."
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We survey the current state of the art in geometric constraint solving. Both 2D and 3D constraint solving is considered, and different approaches are characterized.
As We May Print: New Directions in Output Devices and Computational Crafts for Children
 In Proceedings of Interaction Design and Children 2003
, 2003
"... In recent years, educational technologists and designers have begun to explore a variety of ways in which physical and computational media can be integrated—for instance, through the design of “intelligent toys ” for children. This paper describes our ongoing efforts at exploring a different sort of ..."
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Cited by 6 (1 self)
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In recent years, educational technologists and designers have begun to explore a variety of ways in which physical and computational media can be integrated—for instance, through the design of “intelligent toys ” for children. This paper describes our ongoing efforts at exploring a different sort of physicalcomputational integration, focusing on children’s design activities, output devices, and the notion of “printing out ” more generally. We describe several representative systems under development in our group; each of these systems highlights particular possibilities for exploring and experimenting with output devices for children’s crafts. We also present a set of design heuristics—useful techniques for those educational designers interested in expanding the range and expressiveness of craft activities for children.
Reconfigurations of polygonal structures
, 2005
"... This thesis contains new results on the subject of polygonal structure reconfiguration. Specifically, the types of structures considered here are polygons, polygonal chains, triangulations, and polyhedral surfaces. A sequence of vertices (points), successively joined by straight edges, is a polygona ..."
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This thesis contains new results on the subject of polygonal structure reconfiguration. Specifically, the types of structures considered here are polygons, polygonal chains, triangulations, and polyhedral surfaces. A sequence of vertices (points), successively joined by straight edges, is a polygonal chain. If the sequence is cyclic, then the object is a polygon. A planar triangulation is a set of vertices with a maximal number of noncrossing straight edges joining them. A polyhedral surface is a threedimensional structure consisting of flat polygonal faces that are joined by common edges. For each of these structures there exist several methods of reconfiguration. Any such method must provide a welldefined way of transforming one instance of a structure to any other. Several types of reconfigurations are reviewed in the introduction, which is followed by new results. We begin with efficient algorithms for comparing monotone chains. Next, we prove that flat chains with unitlength edges and angles within a wide range always admit reconfigurations, under the dihedral model of motion. In this model, angles and edge lengths are preserved. For the universal
Output Devices, Computation, and the Future of Mathematical Crafts
 International Journal of Computers in Mathematical Learning
, 2002
"... As I write this sentence, I am glancing over at the color printer sitting beside my screen. In the popular jargon of the computer industry, that printer is called a "peripheral"—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ..."
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Cited by 5 (2 self)
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As I write this sentence, I am glancing over at the color printer sitting beside my screen. In the popular jargon of the computer industry, that printer is called a &quot;peripheral&quot;—which, upon reflection, is a rather odd way to describe it. What, precisely, is it peripheral to? If the ultimate
Shop Class for the Next Millennium: Education Through ComputerEnriched
, 1998
"... Abstract: In this paper we use our experiences with the HyperGami program as a springboard for a broader look at the future of computationallyenriched handicrafts. HyperGami is an educational application for the design and construction of mathematical models and sculptures in paper; as such, it ser ..."
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Abstract: In this paper we use our experiences with the HyperGami program as a springboard for a broader look at the future of computationallyenriched handicrafts. HyperGami is an educational application for the design and construction of mathematical models and sculptures in paper; as such, it serves as a source of examples and insights for the more general problem of how to integrate the “hightech ” features of computation with the “lowtech ” features of traditional craft materials in education. We begin by describing the HyperGami program, focusing on those features that were designed in response to problems encountered by papercrafters; we illustrate the program’s capabilities by presenting some of our own and our students ’ papercraft designs; and we describe our initial steps in implementing elements of HyperGami on the World Wide Web. In the closing sections of the paper, we explore the broader educational issues involved in integrating computation and handicrafts; and we conclude with a discussion of how physical objects could play a role in a future “educational object economy.”
On Serlio's constructions of ovals
, 2001
"... In his celebrated Tutte l'Opere d'Architettura published over the period 15371575 Sebastiano Serlio introduced four techniques for constructing ovals which have thereafter been applied by many architects across Europe. Using various geometric forms (i.e. the triangle, square, and circle) ..."
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In his celebrated Tutte l'Opere d'Architettura published over the period 15371575 Sebastiano Serlio introduced four techniques for constructing ovals which have thereafter been applied by many architects across Europe. Using various geometric forms (i.e. the triangle, square, and circle) as a basis they produced ovals made up from four circular arcs. This paper analyses both Serlio's constructions and some of the many possible alternatives and evaluates their accuracy in terms of the ovals' approximations to an ellipse. 1
EdgeUnfolding Nested Polyhedral Bands
, 2006
"... A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the ot ..."
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Cited by 4 (3 self)
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A band is the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. The intersection of the planes and the polyhedron produces two convex polygons. If one of these polygons contains the other in the projection orthogonal to the parallel planes, then the band is nested. We prove that all nested bands can be unfolded, by cutting along exactly one edge and folding continuously to place all faces of the band into a plane, without intersection.
The Homespun Museum: Computers, Fabrication, and the Design of Personalized Exhibits
 In Proc. C&C’05 Conference on Creativity & Cognition
, 2005
"... The traditional view of the “home computer ” is as a selfcontained appliance: computation, on this view, is something that takes place within a desktop box, and that produces interesting visual effects only on a screen. In this paper, we argue that one can alternatively view “the computer ” through ..."
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The traditional view of the “home computer ” is as a selfcontained appliance: computation, on this view, is something that takes place within a desktop box, and that produces interesting visual effects only on a screen. In this paper, we argue that one can alternatively view “the computer ” through its tangible effects on larger settings: that is, the computer can be imagined as the heart of a creative workshop centered within the home or classroom. The advent of accessible fabrication devices, as well as small computers that can be embedded in craft items, permits users to think of the room at large as a place in which computationallyenriched or computationallydesigned &quot;exhibits &quot; of various types may be displayed. We illustrate this idea with a variety of projects undertaken within our laboratory. Author Keywords Computational crafts, fabrication devices, embedded computation. ACM Classification Keywords H5.m. Information interfaces and presentation (e.g., HCI):
Unfolding Polyhedral Bands
"... A band is de ned as the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band ..."
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Cited by 3 (2 self)
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A band is de ned as the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band into the plane, without causing intersections. We prove that for a speci c type of band there exists an appropriate edge to cut so that the band may be unfolded.
Orihedra: Mathematical Sculptures in Paper
 International Journal of Computers for Mathematical Learning
, 1997
"... Mathematics, as a subject dealing with abstract concepts, poses a special challenge for educators. In students ' experience, the subject is often associated with (potentially) unflattering adjectives—"austere", "remote", "depersonalized", an ..."
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Cited by 2 (0 self)
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Mathematics, as a subject dealing with abstract concepts, poses a special challenge for educators. In students ' experience, the subject is often associated with (potentially) unflattering adjectives—&quot;austere&quot;, &quot;remote&quot;, &quot;depersonalized&quot;, and so forth. This paper describes a computer program named HyperGami whose purpose is to alleviate this harsh portrait of the mathematical enterprise. HyperGami is a system for the construction of decorated paper polyhedral shapes; these shapes may be combined into larger polyhedral sculptures, which we have dubbed &quot;orihedra. &quot; In this paper, we illustrate the methods by which orihedra may be created from HyperGami solids (using the construction of a particular sculpture as an example); we describe our experiences with elementary and middleschool students using HyperGami to create orihedra; we discuss the current limitations of HyperGami as a sculptural medium; and we outline potential directions for future research and software development.