Geometry

The domes of Florence offer a big architectural system to be investigated, and its big heritage value has brought to an investigation, which moved from general aspects to particular ones. It started from the accurate cataloguing of all of the churches' domes in Florence, and it focused on the analysis of one of the most important artist of the Italian renaissance: Filippo Brunelleschi. The study of life and works of this architect was conducted through the documents, which are preserved at the Opera del Duomo, through

This paper will discuss properties and results that arise when studying a quite lesser known point in Geometry, the Poncelet point. The Poncelet point is very powerful when it comes to studying Projective geometry, but has suprising applications in Euclidean geometry as well. As such, this paper will be exploring this point in both a projective and euclidean light.

The article discusses the handwritten revisions and drawn additions by Albrecht Dürer in his own copy of the treatise on geometry, Underweysung der Messung (1525). Situating Dürer’s interest in mathematics within the scholarly milieu of Renaissance Nuremberg, the article addresses the shifts in style and content that Dürer proscribes and offers new perspectives on the artist’s relation to his own late work. The article concludes by displaying several drawings bound into the edition by Dürer that illustrate variations on perspectival apparatuses. These lesser known drawings illuminate the evolution of Dürer’s conceptualization of the dynamics between artist and subject, as well as the tools used to facilitate this interaction.

The digital waveguide mesh is an extension of the onedimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two-and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. The original rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. Alternative geometries, such as the triangular mesh, have been proposed previously to improve the performance of the mesh. In this paper, we show that the dispersion problem may be reduced using various other techniques. These methods include multidimensional interpolation, optimization of the point-spreading function, and frequency warping. We compare the accuracy and computational complexity of these techniques in the two-dimensional (2-D) case and conduct numerical simulations of a membrane. A rectangular mesh using second-order Lagrange interpolation can be implemented without multiplications, but its accuracy is worse than that of other enhanced structures. The most accurate technique in terms of the relative frequency error is the warped triangular mesh whose maximum error is 0.6%. The warped rectangular mesh with optimized weighting coefficients is not as exact, but still offers a 1.2% accuracy.

Mathematical Reviews:

MR2677125 Reviewed Easley, David; Kleinberg, Jon Networks, crowds, and markets. Reasoning about a highly connected world. Cambridge University Press, Cambridge, 2010. xvi+727 pp. ISBN: 978-0-521-19533-1 (Reviewer: Sandra L. Arlinghaus) 91-01 (05C82 68M11 68R10 91B24 91D30)

Sum frequency generation (SFG) vibrational spectroscopy has been applied to investigate surface structures of an amphiphilic surface-active block copolymer (SABC) film deposited on a CaF 2 substrate, in air and in water in situ. Developed as a surface-active component of an antifouling coating for marine applications, this amphiphilic triblock copolymer contains both hydrophobic fluorinated alkyl groups as well as hydrophilic ethoxy groups. It was found that surface structures of the copolymer film in air and in water cannot be probed directly using the SFG experimental geometry we adopted because SFG signals can be contributed from the polymer/air (or polymer/water) interface as well as the buried polymer/CaF 2 substrate interface. Using polymer films with varied thicknesses, structural information about the polymer surfaces in air and in water can be deduced from the detected SFG signals. With SFG, surface restructuring of this polymer has been observed in water, especially the methyl and methylene groups change orientations upon contact with water. However, the hydrophobic fluoroalkyl group was present on the surface in both air and water, and we believe that it was held near the surface in water by its neighboring ethoxy groups.

This paper describes an integrated M M W radar and vision sensor system for autonomous on-mad navigation. The radar sensor has a range of approximately 200 metres and uses a linear array of receivers and wavefmnt reconstruction techniques to compute range and bearing of objects within thefield of view. It is integrated with a vision based lane keeping system to accurately detect and classify obstacles with respect to the danger they pose to the vehicle and to execute required avoidance maneuvres. I ,

In this paper, a new algorithm for Automatic License Plate Localisation and Recognition (ALPR) is proposed on the basis of isotropic dilation that can be achieved using the binary image Euclidean distance transform. In a blob analysis problem, any two Region of Interest (RoIs) that is discontinuous are typically treated as separate blobs. However, the proposed algorithm combine with Connected Component Analysis (CCA) are coded to seek for RoI within a certain distance of other RoI to be treated as non-unique. This paper investigates the design and implementation of several pre-processing techniques and isotropic dilation algorithm to classify moving vehicles with different backgrounds and varying angles. A multi-layer feed-forward back-propagation Neural Network is used to train the segmented and refined characters. The results obtained can be used for implementation in the vehicle parking management system.

A detailed spectroscopic and photophysical study has been carried out on a series of heterocyclic compounds-known to display nonlinear optical properties-consisting on a electron donating thienylpyrrolyl p-conjugated system functionalized with an electron acceptor benzothiazole moiety. The absorption, emission and triplet-triplet absorption together with all relevant quantum yields (fluorescence, intersystem crossing and internal conversion), excited state lifetimes and the overall set of deactivation rate constants (k F , k IC and k ISC) were obtained in solution at room (293 K) and low (77 K) temperature. The optimized ground-state molecular geometries for the compounds together with the prediction of the lowest vertical one-electron excitation energy and the relevant molecular orbital contours for the compounds were also determined using density functional theory (DFT) at the B3LYP/3-21G* level. The experimental results showed that the photophysical properties are influenced by the relative position of the pyrrole and thiophene relative to the benzothiazole group.

Synthetic Aperture Radar (SAR) images are strongly corrupted by the speckle noise due to random electromagnetic waves interference. The speckle noise reduces the quality of images and makes their interpretation and analysis really difficult, so it's necessary to filter images to remove the noise in order to preserve as much as possible the most important features of the signals. To achieve this goal, in this paper we present an efficient method that reduces the speckle noise in SAR images, based on the Contourlet Transform (CT). The CT is a new image decomposition scheme that provides sparse representation of the data, constructed by combining two successive stages, applying in first a Laplacian pyramidal decomposition followed by a directional filter bank. This non-linear approach is designed to give a good representation of the geometrical content of the natural images. Recently, the Stationary version of the Contourlet Transform (SCT) has been proposed to preserve the shift-invariant property. In the present paper, we explore two different de-noising methods: the Bayesian Shrinkage based on a weighting factor that reduces noise by using the contourlet coefficients, and the Soft Thresholding based on the choice of the threshold that ensures adaptation to the noiseless signals. Hence, we present a comparative study of the results obtained through the SCT considering different stages of decomposition's levels and different kind of filters, and the Lee Adaptive Filter. A performance evaluation is realized to validate our methods.

Systematic problem solving contributes to the conscious and lasting assimilation of the theory of geometry, helps to see its practical value, and forms key competencies in the field of geometry. Geometric tasks, like other mathematical tasks, perform educational, developmental and teaching functions.

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours, except for the technical details of the formalism. Following the logic of our article point by point, Lim and Leek (a) defined probabilistic expectations about the geometry of smooth contours (which they based on differential contour geometry, while we used a discrete approximation--the only essential difference in their approach), (b) assumed that information along the contour was proportional to the negative logarithm of probability, following standard information theory, and then (c) extended this formulation to closed contours. We analyze what they described as errors in our approach, all of which rest on mathematical misunderstandings or ...

We survey the Hilbert geometry of convex polytopes. In particular we present two important characterisations of these geometries, the first one in terms of the volume growth of their metric balls, the second one as a bi-lipschitz class of the simplexe's geometry.

This paper addresses the problem of grasping and manipulating a polygonal object with three discshaped robots capable of translating in arbitrary directions in the plane. The main novelty of the proposed approach is that it does not assume that contact is maintained during the execution of the grasping/manipulation task. Nor does it rely on detailed (and a priori unveri able) models of friction or contact dynamics. Instead, the range of possible object motions for a given position of the robots is characterized in con guration space. This allows the construction of manipulation plans guaranteed to succeed under the weaker assumption that jamming does not occur during the task execution.

A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It i...

Magnetic field distributions from flat conductor electromagnetic surface acoustic wave transducers have been investigated for meander and grating line geometries. Expressions are derived for magnetic fields and inductance of electromagnetic transducers, and for space harmonic amplitudes of surface currents induced in a metal ground plane. Lift off, that is, separation gap between conductors and ground plane, and transducer geometry are accounted for in the theory. Experimental measurements of inductance are presented and compared with predicted inductance values, and good agreement is found.

Checking railway status is critical to guarantee high operating safety, proper maintenance schedule, and low maintenance and operating costs. This operation consists of the analysis of the rail profile and level as well as overall geometry and ondulation. Traditional detection systems are based on mechanical devices in contact with the track. Innovative approaches are based on laser scanning and image analysis. This paper presents an efficient composite technique for track profile extraction with real-time image processing. High throughput is obtained by algorithmic prefiltering to restrict the image area containing the track profile, while high accuracy is achieved by neural reconstruction of the profile itself.

Multi-axis slicing for solid freeform fabrication (SFF) manufacturing process can yield non-uniform thickness layers, or 3-D layers. Using the traditional parallel layer construction approach to build such a layer leads to a staircase which requires machining or other post processing to form the desired shape. This paper presents a direct 3-D layer deposition approach. This approach uses an empirical model to predict the layer thickness based on experimental data. The toolpath between layers is not parallel; instead, it follows the final shape of the designed geometry and the distance between the toolpath in the adjacent layers varies at different locations. Directly depositing a 3-D layer not only eliminates the staircase effect, but also improves the manufacturing efficiency by shortening the deposition and machining times. A single track deposition experiment has demonstrated these advantages. Thus, it is a beneficial addition to the traditional parallel deposition method.

This article presents an alternative way of analyzing the van Hiele level of students' geometrical reasoning. We evaluate the students' answers, taking into account the van Hiele level they reflect and their mathematical accuracy. This gives us a description of how accomplished the students are in applying the procedures associated with each of the van Hiele levels and allows us to determine the students' degree of acquisition of the van Hiele levels. In this way we obtain a clearer picture of the students' geometrical reasoning than with the traditional assignment of one van Hiele level to the learners. An example of the application of this method is provided: We describe a test that evaluated students' ability to reason in three-dimensional geometry, some responses of students (9 eighth-grade pupils and 41 future primary school teachers), and the classification of their responses using our method.

A novel exact derivation for the kinetic constant of a bimolecular reaction according to three well-known models of collision theory is reported. The use of probability density functions, with the introduction of a novel geometry to study the collision process, allows simplifying the derivation to such an extent, that, for a proper statistical background, it is is possible to recover the line-of-centers and the angular dependent line-of-centers models in no more than a couple of lectures. Although the derivation is introduced to recover the temperature-dependent kinetic constant, it is shown that the energy-dependent reactive cross section can be recovered as well. A possible confusion in the interpretation of the pre-exponential factor is commented.

Geometric hashing is a model-based recognition technique based on matching of transformation-invariant object representations stored in a hash table. In the last decade, a number of enhancements have been suggested to the basic method improving its performance and reliability. One of the important enhancements is rehashing, improving the computational performance by dealing with the problem of non-uniform occupancy of hash bins. However, the proposed rehashing schemes aim to redistribute the hash entries uniformly, which is not appropriate for Bayesian approach, another enhancement optimizing the recognition rate in presence of noise. In this paper, we derive the rehashing for Bayesian voting scheme, thus improving the computational performance by minimizing the hash table size and the number of bins accessed, while maintaining optimal recognition rate.

This work is aimed at studying the problem of controlling the moment and the orientation of a robot manipulator whose end effector is in contact with a compliant environment. Differently from classical operational space formulations, a geometrical approach is pursued where orientation displacements are described in terms of unit quaternions. Regulation to a constant desired moment and tracking of a time-varying desired orientation trajectory is achieved, and the convergence of the closed-loop system is analyzed. Simulation results for a six-joint industrial robot are developed and an experimental test is carried out to demonstrate the effectiveness of the proposed approach in a practical contact task.

Camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3D apparatus (two or three planes orthogonal to each other or a plane undergoing a pure translation, etc.), 2D objects (planar patterns undergoing unknown motions), and 0D features (self-calibration using unknown scene points). Yet, this paper proposes a new calibration technique using 1D objects (points aligned on a line), thus filling the missing dimension in calibration. In particular, we show that camera calibration is not possible with free-moving 1D objects, but can be solved if one point is fixed. A closed-form solution is developed if six or more observations of such a 1D object are made. For higher accuracy, a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate. Singularities have also been studied. Besides the theoretical aspect, the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other, where the calibration objects are required to be visible simultaneously.

As Euclid said, “There is no royal way to learn geometry.” However, we can create many paths to geometry with matchsticks. The book consists of thirteen chapters. The importance of learning geometry with matchsticks is mentioned in the introduction, which is the first part of the book. In the second part, questions about “resfebe”, word questions in the third part, and “ikara” game questions are included in the fourth part. In the fifth part of the book, triangle questions are mentioned. In the sixth chapter, the square questions are included, and this chapter is the most comprehensive part of the book. In the seventh chapter, rectangular and rhombus, in the eighth chapter cube, and in the ninth chapter, polyomino questions were mentioned. In the tenth chapter of the book, the questions of the area, the questions of dividing the figures into identical parts in the eleventh chapter, and the questions of finding the number of polygons and solid objects in the twelfth chapter are included. In the last part of the book, the answers to the 400 questions in the book were shared with the readers. Hoping that it will contribute to geometry as much as matchstick ...


Euclid’in söylediği gibi “Krallara özgü bir geometri öğrenme yolu yoktur.” ancak kibrit çöpleriyle geometriye giden birçok yol oluşturabiliriz.
Kitap on üç bölümden oluşmaktadır. Kitabın birinci bölümü olan giriş bölümünde kibrit çöpleriyle geometri öğrenmenin öneminden bahsedilmiştir. İkinci bölümde resfebe ile ilgili sorulara, üçüncü bölümde kelime sorularına, dördüncü bölümde ise ikara oyunu sorularına yer verilmiştir. Kitabın beşinci bölümünde ise üçgen sorularına değinilmiştir. Altıncı bölümde ise kare sorularına yer verilmiş olup bu bölüm kitabın en kapsamlı kısmıdır. Yedinci bölümde dikdörtgen ve eşkenar dörtgen, sekizinci bölümde küp, dokuzuncu bölümde ise polyomino sorularından bahsedilmiştir. Kitabın onuncu bölümünde alan sorularına, on birinci bölümünde şekilleri özdeş parçalara ayırma sorularına, on ikinci bölümde ise çokgenlerin ve katı cisimlerin sayısını bulma sorularına yer verilmiştir. Kitabın son bölümünde ise kitaptaki 400 sorunun cevapları okuyucularla paylaşılmıştır.
Geometriye kibrit çöpü kadar katkısı olması temennisiyle…

Une comparaison est effectuee entre les facons employees en photogrammetrie et en vision par ordinateur pour traiter les problemes lies a l'acquisition de la 3D a partir d'images stereoscopiques. Le formalisme adopte, assez different, est presente, et quelques perspectives d'evolution en sont deduites.

Recently the possibility of an earthquake has become one of the most important subjects in lots of countries especially in Turkey. For that reason, the possibility of an earthquake gains ground due to its devastating physical and psychological effects. Because of these physical losses and its psychological effects, people who experience the earthquake generally become sensitive and provident. Although disaster management had been established before the earthquake, the studies after the earthquake prove the fact that decreases in the loss of lives is inadequate. In this study, the aerial photographs have used which have been obtained before and after the earthquake. An algorithm is developed that determines the damaged buildings as semi-automatic. The principle of this study is analyzing the buildings' image histograms and determining their conditions. Gölcük and Adapazarı regions before and after the earthquake have been used for the analysis of the image histograms that belong to the buildings in the aerial photographs. Our empirical results have shown that the histograms of the undamaged and damaged buildings have different forms. For this reason, utilizing the histogram analysis, the conditions of the damaged buildings have determined by using a semi-automatic process. The important precondition for this study is the digital maps of the study area to be in existence. Briefly, to form the histograms, the coverage areas of the buildings that are after the earthquake photographs in vector format are found and the image histograms are calculated from those areas. The purpose is to determine the damaged buildings quickly during the earthquake and contribute to the disaster management. It is thought that, through the results that are to be obtained, it will be possible to direct the rescue mission correctly, estimate the number of loss of lives and take healthy precautions.

Most of the electromagnetic problems can be reduced down to either integrating oscillatory integrals or summing up complex series. However, limits of the integrals and the series usually extend to infinity. In addition, they may be slowly convergent. Therefore, numerically efficient techniques for evaluating the integrals or for calculating the sum of infinite series have to be used to make the numerical solution feasible and attractive. In the literature, there are a wide range of applications of such methods to various EM problems. In this paper, our main aim is to critically examine the popular series transformation (acceleration) methods which are used in electromagnetic problems and compare them by numerical examples.

In this study we seek to identify brain and body activities that correlate in valid and reliable manners, and with a high degree of statistical significance, with different aspects of geometrical image-based perception and reasoning. In so doing, we seek a better understanding of cognitive processes associated with geometrical image-based learning, instruction, and assessment in mathematics education, and to contribute to extending multidisciplinary boundaries of educational research.

This paper considers the problem of direction-ofarrival (DOA) estimation for multiple uncorrelated plane waves incident on so-called "fully augmentable" sparse linear arrays. In situations where a decision is made on the number of existing signal sources (m m m) prior to the estimation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case where m m m is less than the number of antenna sensors (M M M), a new approach called "MUSIC-maximum-entropy equalization" is proposed to improve DOA estimation performance in the "preasymptotic region" of finite sample size (N N N) and signal-tonoise ratio. A full-sized positive definite (p.d.) Toeplitz matrix is constructed from the M M M 2 2 2M M M direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m m m-variate signal eigensubspace ("signal subspace truncation"). When m m m M M M, Cramér-Rao bound analysis suggests that the minimal useful sample size N N N is rather large, even for arbitrarily strong signals. It is demonstrated that the well-known direct augmentation approach (DAA) cannot approach the accuracy of the corresponding Cramér-Rao bound, even asymptotically (as N N N ! ! !1 1 1) and, therefore, needs to be improved. We present a new estimation method whereby signal subspace truncation of the DAA augmented matrix is used for initialization and is followed by a local maximum-likelihood optimization routine. The accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios (m m m M M M) presented.

Geometry is taught as a subject-matter in mathematics courses at elementary school level, and as an independent course at secondary school level in Turkish education system. When the success levels of students regarding these two subjects are examined, it can be seen that there are differences. Anxiety is an important variant on success in mathematics. But whereas geometry is considered as a different field from mathematics by the students, mathematics anxiety cannot cover geometry anxiety completely and that geometry anxiety can be observed separately from mathematics anxiety. Thus the aim of this study is to develop a scale for secondary school level students in order to determine their anxiety towards geometry.