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“…The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of e and \pi, of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.…”
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“…Experiments using an initial prototype to trace a continuous straight edge have quantified the user's ability to discriminate the angle of the edge, a potentially useful feature for higher levels analysis of the visual scene.…”
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“…Following open reduction of the FDP avulsion fracture and fixation was achieved with a 0.9 mm one edge hooked Kirschner wire under fluoroscopy control. The straight edge of the wire was driven out in a central position in sterile nail matrix just distal to lunula. …”
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“…We report on a novel method to interrupt this transition point by using pinking shears, which are dressmaking scissors with saw-toothed blades that create a chevron pattern instead of a straight edge. We describe a case where the pinking shears were utilized on a split skin graft and Integra for reconstruction of the skin on a volar forearm. …”
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“…The generating sets of [Image: see text] have been enumerated which consist of integral four-dimensional vectors with components −1, 0, 1 and allow Cayley graphs without edge intersections in a straight-edge embedding in a four-dimensional Euclidean space. …”
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“…The thought experiment leads to the discovery and realization from the two protagonists that Euclidean geometry is possible using sensorimotor functions with tools called a straight edge and compass or simply a rope with knots. …”
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“…With the increase of annealing temperature, the surface morphology changes from corrugation to straight edge, the number of screw dislocations changes from none to numerous, and the surface atomic structure changes from disordered to ordered structures (with many reconstructions). …”
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“…The results indicate that the PCD tool with the straight edge, inclined peripheral tooth shape produces the smallest total cutting force and less delamination (shortest and lowest number of delaminated fibres) at both fresh and worn states. …”
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“…Through this investigation, the physical confinement of donor–acceptor type SP chains in a continuous nanoscale network structure surrounded by polystyrenes is shown to induce structural ordering with more straight edge‐on stacked SP chains. Hereby, high‐performance and transparent organic field‐effect transistors with a hole mobility of ≈5.4 cm(2) V(–1) s(–1) and an average transmittance exceeding 72% in the visible range are achieved.…”
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“…We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. …”
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“…A piezoelectric transducer is bonded on the straight edge of the hole to generate the incident wave. …”
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“…Methods: We compared the rehydrated and fresh-preserved corneas by microscopy following Victus-Tecnolas FSL treatment for straight-edge anterior lamellar keratoplasty (ALK). The corneas were dehydrated at room temperature under a laminar-flow hood. …”
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“…The filter operation is based on a straight-edge Y-type hexagonal ferrite resonator symmetrically coupled to the input and output microstrip transmission lines. …”
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“…The anterior upper lobe (AUL) sign, exuberant honeycombing (EHC), and straight edge (SE) sign are recently described computed tomography (CT) signs in CTD-related UIP. …”
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“…Maximum deflection distance (maximum distance from a straight edge that was placed from the tip of the snout to the poll of the head) was not different (P = 0.10) between PC MARKET BARROWS (3.31 ± 0.10 cm) and IC BOARS (3.08 ± 0.10 cm). …”
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“…This could occur through disrupting the radial symmetry of optic flow via the aperture effect (i.e. generation of false motion cues by straight edges), or through spatio-temporal aliasing (i.e. misregistration of repeated features) of evenly spaced stripes. …”
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“…On the other hand, the effect of increasing the embossing temperature on the morphology of nanogrooves agrees with the master mold, and the crests between the nanogrooves form straight edges. It should be noted that the micro-embossing temperature also strongly influences the transferability of nanopatterns on an acrylic film. …”
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“…Morphologically, marginal plates were revealed to consist of rectangular straight-edged sheets, exhibiting a defined crystalline lattice structure. …”
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