Geometry

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.

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)

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.

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 ...

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...

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.

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.

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.