A Geometrical Ensemble to Generate the Squaring of the Circle

Engineer Helmut Sander reflects on the impossibility of squaring the circle and the irrational number π, and provides a geometric construction that approximates the operation.     

Squaring the Circle: Marriage of Heaven and Earth

It is impossible to construct circles and squares of equal areas or perimeters precisely, for circles are measured by the incommensurable value pi (π) and squares by rational whole numbers. But from early times, geometers have attempted to reconcile these two orders of geometry. “Squaring the circle” can represent the union of opposing eternal and finite qualities, symbolizing the fusion of matter and spirit and the marriage of heaven and earth. In this column, we consider various methods for squaring the circle and related geometric constructions.     

The Squaring of the Circle in two Early Norwegian Cathedrals?

The squaring of the circle is impossible, but it can be represented geometrically. One such construction is similar to a diagram used to analyze two early Norwegian cathedrals. Further investigation revealed that it was not quite that simple. However, this pursuit revealed some alternative, but related possibilities, including a way of combining √2 and √5 – albeit approximately.     

From Circle to Ellipse: Footnotes to a Photographic Essay

In linguistics, ellipsis (from the Greek: élleipsis, “omission”) or elliptical construction refers to the omission from a clause of one or more words that would otherwise be required by the remaining elements. Photography encapsulates a wide range of experiential possibilities with the rhetoric of visualization and discursivity. The medium constantly reminds us of the basic geometric principles of perspective: perceived rather than measured, brought into consciousness through basic knowledge without need to name the phenomenon. It is the image that fills the gap, pronouncing elliptically what we feel, see and conclude, while the subject recounts the story.     

Patterns on a Surface: The Reconciliation of the Circle and the Square

The theory of heat flow on a surface shows that any curvilinear quadrilateral can be ‘tiled’ with curvilinear squares of varying size. This paper demonstrates a simple numerical technique for doing this that can also be applied to shapes other than quadrilaterals. In particular, any curvilinear triangle can be tiled with curvilinear equilateral triangles.     

Revisiting the Merton Problem: from HARA to CARA Utility

Computational Economics - This paper revisits the classical Merton problem on the finite horizon with the constant absolute risk aversion utility function. We apply two different methods to derive...     

Four Approximations for Finding the Golden Section of a Circle’s Circumference from the Square Root Two Rectangle

Geometer Mark Reynolds discusses four approximatons for finding the Golden Section of the circumference of a circle from the root-2 rectangle.     

Squaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal ones

This paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a β-contractive ellipsoidal set , the key idea is to construct a polyhedral set that lies between the ellipsoidal sets and . A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired polyhedral set. The problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.     

Revisiting the uncanny valley theory: Developing and validating an alternative to the Godspeed indices

Mori (1970) proposed a hypothetical graph describing a nonlinear relation between a character’s degree of human likeness and the emotional response of the human perceiver. However, the index construction of these variables could result in their strong correlation, thus preventing rated characters from being plotted accurately. Phase 1 of this study tested the indices of the Godspeed questionnaire as measures of humanlike characters. The results indicate significant and strong correlations among the relevant indices (Bartneck, Kuli?, Croft, & Zoghbi, 2009). Phase 2 of this study developed alternative indices with nonsignificant correlations (p > .05) between the proposed y-axis eeriness and x-axis perceived humanness (r = .02). The new humanness and eeriness indices facilitate plotting relations among rated characters of varying human likeness.     

Squaring down and the problems of almost zeros for continuous-time systems

In this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains. We derive the minimal gain of the precompensator to achieve such a square system. If the gain of this precompensator is too large then we derive an explicit trade-off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system.     

爱敏捷，爱自由

仲夏之夜,一个五层楼的天台上传出轻快的音乐,一群年轻人聚集在这里,桌子上摆放着各种颜色的酒水和饮料,中间的两个大横桌上摆放了各种精致的美食。一阵欢快的笑声传来,寻声望去,天台的一角有一个桌上足球案,几个年轻人正在激烈的对逐。而天台的另一侧则摆放着两个红彤彤的炭火炉。     

From bytecode to JavaScript: the Js_of_ocaml compiler

We present the design and implementation of a compiler from OCaml bytecode to JavaScript. The compiler first translates the bytecode into a static single‐assignment intermediate representation on which optimizations are performed, before generating JavaScript. We believe that taking bytecode as an input instead of a high‐level language is a sensible choice. Virtual machines provide a very stable API. Such a compiler is thus easy to maintain. It is also convenient to use, and it can just be added to an existing installation of the development tools. Already‐compiled libraries can be used directly, with no need to reinstall anything. Finally, some virtual machines are the target of several languages. A bytecode to JavaScript compiler would make it possible to retarget all these languages to Web browsers at once. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimizing Sensing: From Water to the Web

Where should we place sensors to quickly detect contamination in drinking water distribution networks? Which blogs should we read to learn about the biggest stories on the Web? Such problems are typically NP-hard in theory and extremely challenging in practice. The authors present algorithms that exploit submodularity to efficiently find provably near-optimal solutions to large, complex real-world sensing problems.     

From MT to LREV: managing the transition

Machine Translation -     

Revisiting the notion of function

Functions play a central role in type theory, logic and computation. We describe how the notions of functionalisation (the way in which functions can be constructed) and instantiation (the process of applying a function to an argument) have been developed in the last century. We explain how both processes were implemented in Frege’s Begriffschrift, Russell’s Ramified Type Theory, and the λ-calculus (originally introduced by Church) showing that the λ-calculus misses a crucial aspect of functionalisation. We then pay attention to some special forms of function abstraction that do not exist in the λ-calculus and we show that various logical constructs (e.g., let expressions and definitions and the use of parameters in mathematics), can be seen as forms of the missing part of functionalisation. Our study of the function concept leads to: (a) an extension of the Barendregt cube [4] with all of definitions, Π-reduction and explicit substitutions giving all their advantages in one system; and (b) a natural refinement of the cube with parameters. We show that in the refined Barendregt cube, systems like A , LF, and ML, can be described more naturally and accurately than in the original cube.     

Databases to the Web: From Static to Dynamic on the Express

SUMMARY

The need to deliver current data on periodical holdings and electronic resources led the staff at Kennesaw State University's Sturgis Library to develop database-driven dynamic Web pages. The project's success was based on the incorporation of skills, technologies and hardware that were already in place in the library with Allaire's ColdFusion Express, a free, feature-limited version of ColdFusion Web application server.     

Revisiting technological pedagogical content knowledge: Exploring the TPACK framework

This study examines the nature of technological pedagogical content knowledge (TPACK) through the use of a factor analysis. Using a survey with 24 items designed to measure each of the areas described by the TPACK framework, and measuring the responses of 596 online teachers from across the United States, data suggest that while the framework is helpful from an organizational standpoint, it is difficult to separate out each of the domains, calling into question their existence in practice. Three major factors become evident, but rather than being comprised of pedagogy, content, and technology, the only clear domain that distinguishes itself is that of technology. This research examines the validity of the TPACK model and suggests that measuring each of these domains is complicated and convoluted, potentially due to the notion that they are not separate.     

AVS-M: From Standards to Applications

AVS stands for the Audio Video coding Standard Workgroup of China, who develops audio/video coding standards as well as system and digital right management standards. AVS-M is the AVS video coding standard targeting for mobile multimedia applications. Besides the coding specification, AVS also developed the file format and Real-time Transport Protocol （RTP） payload format specifications to enable the application of AVS-M video in various services. This paper reviews the high-level coding tools and features of the AVS-M coding standard as well as the file format and payload format standards. In particular, sixteen AVS-M high-level coding tools and features, which cover most of the high-level topics during AVS-M standardization, are discussed in some detail. After that, the error resilience tools are briefly reviewed before the file format and RTP payload format discussions. The coding efficiency and error resiliency performances of AVS-M are provided finally. H.264/AVC has been extensively used as a comparison in many of the discussions and the simulation results.     

Profiling: From data to knowledge

Profiling is not about data but about knowledge. It provides a crucial technology in a society that is flooded with noise and information. Profiling is another term for sophisticated pattern recognition, and the enabling technology for Ambient Intelligence. It confronts us with a new type of inductive knowledge, inferred by means of automated algorithms. To the extent that decisions that impact our lives are based on such knowledge, we need to develop the means to make this knowledge accessible for individual citizens and provide them with the legal and technological tools to anticipate and contest such knowledge or challenge its application.