With a few exceptions, all psychology careers will require a doctorate degree, which takes an average of 8.
Practice On the Spline: A Brief History of the Computational Curve Full Some architects herald the adoption of freeform curvilinear design and the utilization of computer-aided manufacturing as cutting edge, or even avant-garde.
While it may be so within the confines of architectural design and discourse, there is, in fact, nothing essentially new about these technologies. In comparison to our counterparts in other fields, architects are, in fact, behind the curve. This article seeks to addresses this deficit of knowledge by summarizing the ingenious development of the computational curve, which occurred in other industries.
Any designer who draws curves with only a few clicks of the mouse, may benefit from knowing how this technology — which we now take for granted — was developed.
The need to compute curved 3D surfaces with the assistance of computer numerically controlled CNC manufacturing was the very impetus for the first computer aided design CAD software over half a century ago, principally developed in the automotive and aerospace industries.
Digital animators in the entertainment industry developed methods of intuitively smoothing topologically ambiguous forms. These solutions have migrated into the software tools architects use today. However, the history of curvature obviously long predates the computational era.
Curvature has always played an important structural role in buildings, evident in the Roman arches and domes that remain standing to this day. Curvature has also inflected architecture with aesthetic refinement.
For example, the use of entasis in Greek antiquity made columns appear to bulge under the strain of their load. It heralded in a renaissance of curvaceous formalism and broadcasted the arrival of the contemporary digital architectural era to mainstream culture.
Given the current vogue for freeform surfaces in architecture, as well as the wider prevalence of ergonomic forms in our daily lives — from toothbrushes to bike helmets — it seems surprising so little historical research architectural or otherwise has been collected regarding the geometrical underpinnings of 21st century computer-aided design.
From the commonplace to the sublime, the spline delineates contemporary aesthetics curved and straight because it is the lingua franca of the design, engineering, and manufacturing industries.
Most accounts of early computer aided geometric design CAGD come from mostly academic books and papers, written for a highly technical audience within that field. Apart for one or two notable exceptions, i historical developments are presented as an evolution of mathematical equations, without much commentary as to their wider importance for humankind.
These texts assume a sophisticated knowledge of advanced mathematics, which, sadly, this author does not possess. Thus, this effort to unravel the story of the spline may be the first nontechnical account written for the intuitive understanding and benefit of the user base — ie.
Demystifying the curve, I hope, will help to develop a better appreciation — perhaps even a connoisseurship — of what has now become a de facto architectural tool: Evidence from Mesolithic settlements, as well as vernacular structures like the native American wigwam, show one of the simplest forms of shelter, formed by ramming poles into a circular formation, bending them inward, and lashing them together to form a sturdy dome-shaped latticework.
By the Mesolithic era, humans had learnt to fashion bows in order to hunt game. As a hunter draws the bow, its two tips are pulled closer, producing greater curvature. As the timber is deformed, it stores elastic potential energy as the wood tries to regain its original straightness.
When a length of wood is flexed, the material on the concave side goes into compression while the convex side is under tension.
In bending, these forces distribute themselves as evenly as possible throughout the length of wood, producing a optimally smooth curve. Evidence of Mesolithic settlements, as well as numerous indigenous cultures, show primitive shelters were constructed in a similar fashion.
The tops of opposite poles were lashed together to form an overall dome-like latticework and covered by animal hides, bark or grass. The native american wigwam is a more recent example. The elasticity of each timber pole produces an arch — an optimal structural shape in compression, imparting strength and rigidity to the crude dome see Figure 1.
Cross sections such as these recorded vessels on contractual order. The outer member marked Fig.
Portions of each cross section are indexed to corresponding pieces on the reconfigurable mould. William Sutherland, The Shipbuilders Assistant: Since ancient history, humankind has harnessed the inherent utility of curved objects, not only to satisfy his basic needs for food and shelter, but also for transportation.
In a crude sense, a boat is the simple inversion of the aforementioned primitive hut.
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Buchanan were all students of Knight at Chicago. Ronald Coase said that Knight, without teaching him, was a major influence on his. Presentations at HFG/George Mason Congressional Briefing on Criminal Justice in the United States, April 24 Complete Video Coverage of 13th Harry Frank Guggenheim Symposium on Crime in America February , John Jay College 42 West 54th Street New York, NY The Harry Frank Guggenheim Foundation.
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Rutgers Physics News Chemistry Professor and member of our Graduate Faculty Wilma Olson has been named a Fellow of the American Physical Society by the Division of Biological Physics. The citation for Wilma reads: "For seminal contributions to understanding nucleic acid structure, properties, and interactions, for leadership in developing important computational methods used to analyze.