Hinged Dissections Exist

We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously without self-intersection to form any polygon in the collection. This result settles the open problem about the existence of hinged dissections between pairs of polygons that goes back implicitly to 1864 and has been studied extensively in the past ten years. Our result generalizes and indeed builds upon the result from 1814 that polygons have common dissections (without hinges). We also extend our common dissection result to edge-hinged dissections of solid 3D polyhedra that have a common (unhinged) dissection, as determined by Dehn's 1900 solution to Hilbert's Third Problem. Our proofs are constructive, giving explicit algorithms in all cases. For a constant number of planar polygons, both the number of pieces and running time required by our construction are pseudopolynomial. This bound is the best possible, even for unhinged dissections. Hinged dissections have possible applications to reconfigurable robotics, programmable matter, and nanomanufacturing.Comment: 22 pages, 14 figure

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Dead and buried… for now: The misdiagnosis of death in enlightenment england

While the concept of the misdiagnosis of death resulting in premature burial sounds like a theme from Hollywood, it was a real circumstance that took place in Western Europe from antiquity through the nineteenth century. Specifically focusing on the England in the eighteenth and early nineteenth centuries, stories of people who had been prematurely diagnosed as dead, prematurely set into their coffin for viewing, and prematurely committed to the grave have been well documented within medical texts, academic books, art, and newspapers articles from the time. These sorts of publications showcased societies awareness of people were being misdiagnosed as dead committed to the earth alive. In response, scholarly physicians began to identify the stages of death with the intent of properly diagnosing people, and only committing those who were absolutely dead to their final resting places. This research is unique to the field in several ways. First, it presents an awareness of premature burial by academic physicians and draws the connection between the problem and the response of the medical community to identify the transitional stages of – and define – death. It focuses on the societal awareness of the misdiagnosis of death, how awareness was obtained, and what was done to help rectify the issue in both the academic medical community and by the public at large. Finally, this thesis presents the first modern statistic comparing the prevalence of premature burial as reported in England. One hundred and fifty-five (155) cases of apparent death and the subsequent premature repercussions (enclosure, burial, interment, or dissection) that had occurred in western Europe and America during the eighteenth century were analyzed in order to create this statistic. These cases were reported in primary and early secondary sources in England. This statistic was then compared against the two hypotheses published in England in the late eighteenth and early nineteenth centuries. Specifically, this modern statistic was contrasted against the hypothesized 10% – 50% of people being buried prematurely in western Europe, as reported by Dr. Samuel Glasse in 1789, and the 10% of people being prematurely buried in England, as reported by Dr. John Snart in 1817. (Author abstract)Salamone, N.C. (2018). Dead and buried… for now: The misdiagnosis of death in enlightenment England. Retrieved from https://academicarchive.snhu.edu/Master ArtsHistoryCollege of Online and Continuing Educatio

Games, puzzles, and computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-153).There is a fundamental connection between the notions of game and of computation. At its most basic level, this is implied by any game complexity result, but the connection is deeper than this. One example is the concept of alternating nondeterminism, which is intimately connected with two-player games. In the first half of this thesis, I develop the idea of game as computation to a greater degree than has been done previously. I present a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games. A deterministic version of Constraint Logic corresponds to a novel kind of logic circuit which is monotone and reversible. At the other end of the spectrum, I show that a multiplayer version of Constraint Logic is undecidable. That there are undecidable games using finite physical resources is philosophically important, and raises issues related to the Church-Turing thesis. In the second half of this thesis, I apply the Constraint Logic formalism to many actual games and puzzles, providing new hardness proofs. These applications include sliding-block puzzles, sliding-coin puzzles, plank puzzles, hinged polygon dissections, Amazons, Kohane, Cross Purposes, Tip over, and others.(cont.) Some of these have been well-known open problems for some time. For other games, including Minesweeper, the Warehouseman's Problem, Sokoban, and Rush Hour, I either strengthen existing results, or provide new, simpler hardness proofs than the original proofs.by Robert Aubrey Hearn.Ph.D

Gold jewellery in Ptolemaic, Roman and Byzantine Egypt.

In 2 volsSIGLEAvailable from British Library Document Supply Centre-DSC:D189616 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Design of an environment-indipendent, tunable 3D DNA-origami plasmonic sensor

DNA origami nanotechnology engineers DNA as the building blocks of newly conceived self-assembled materials and devices. Due to its high degree of customization and its precise spatial addressability, DNA origami provides an unmatched platform for nanoscale structures and devices design. Gold nanoparticles (AuNP) have been largely investigated because of their peculiar optical properties and in particular their localized surface plasmon resonance (LSPR) that modifies significantly the electromagnetic environment in a thin shell around them, and provides a tool with unrivalled potential to tune the local optical properties. The combination of DNA origami frameworks and AuNP into DNA based-plasmonic nanostructures offers a concrete approach for optical properties engineering. It has been successfully applied to design biosensor and to enhance Raman scattering or fluorescence emission. Moreover, it has been exploited to design molecular ruler in which the inter-particle gap is controlled with nanometric precision through the transduction of the conformational changes into univocally detectable optical signals. In this thesis I present my PhD work which aims at the design of an environment-independent AuNP decorated-DNA origami. A tetrahedral DNA shape structure has been selected for its three dimensional robustness and thus a DNA origami prototype has been assembled, characterized with SEM, TEM and AFM to verify the proper folding of the structure. The origami was equipped with an actuator probe which recognizes a specific target oligonucleotide inducing a structural reconfiguration of the tetrahedron. To detect the conformational change triggered by the hybridization event, I functionalized the origami with two gold nanoparticles placed in two opposite facets at a known distance of 10 nm: the change of the interparticle gap is effectively transduced in a LSPR shift. This working principle has been verified with optical extinction measurements and the interparticle distance reduction has been confirmed by SEM imaging and SAXS analysis performed in the SAXS beamline of Elettra Synchrotron, thus confirming that the operation of the device and its transduction mechanism are the same no matter of the external conditions, being them dry, liquid or solid

Washington, D.C. and the Idea of America: A reappraisal of the 1791 plan for the Nation’s Capital

Washington, D.C. was the first American planned city of its size and one of the first attempts at a spatial organisation of the nation’s political objectives. This thesis argues that Pierre L’Enfant’s 1791 plan for the city is a unique example of eighteenth-century speculative development, that assimilated dominant European garden and urban planning traditions, reflected a critical transition in attitudes towards nature and landscape, and produced an unprecedented symbolic framework for the balance of republican values and federal objectives. I use a review of the development of the plan and an analysis of its distribution of space to locate the city within a wider context of continental expansion and the consolidation of national union. In the first part of this thesis I trace three aspects of this context: first, the plan’s relationship to contemporary patterns of land management, survey and territorial settlement; second, the eighteenth-century significance of nature within political thought and the manifestation of these ideas in the garden and landscape precedents available to the architect and his contemporaries; and third, the shift from representations of monarchy to celebrations of presidential authority, evident in L’Enfant’s work. In the second part I conduct a drawn dissection of the structure of the 1791 plan and provide a new interpretation of the primary orientation of the city, the distribution of ceremonial spaces, and the projected character of the commercial and residential urban fabric. Through a conceptual-historical reconstruction of the relationship between the plan for the capital, national expansion and American democracy, my project seeks to recover the significance of Washington, D.C. as a seminal reflection of the collision of a European urban and landscape tradition with the formation of an American political ideology