1,721,004 research outputs found
From Here to Infinity. Tracing the Origin and Development of Projective Geometry
No full textThis monograph traces the development of projective geometry from its Greek origins to the early 20th century. It covers Renaissance perspective studies and insights from the late sixteenth to seventeenth centuries, examining the contributions of Desargues and Pascal.
Most of the book is devoted to the evolution of the subject in the 19th century, from Carnot to von Staudt. In particular, the book offers an unusually thorough appreciation of Brianchon's work, a detailed study of Poncelet's innovations, and a remarkable account of the contributions of Möbius and Plücker. It also addresses the difficult question of the historical relationship between synthetic and analytic points of view in geometry, analyzing the work of prominent synthetic geometers Steiner, Chasles, and von Staudt in detail. The book concludes around 1930, after the synthetic point of view was axiomatized and the analytic point of view became intertwined with algebraic geometry.
Balancing historical analysis with technical precision and providing deep insights into the evolution of the mathematics, this richly illustrated book serves as a central reference on the history of projective geometry
The ideal resolution for generic 3-fat points in P2
No full textAbstractIn this paper we prove that the union Y of the second infinitesimal neighbourhoods of n generic points in P2 is minimally generated for n≠2,3,5, i.e., the maps σk:H0(IY(k))⊗H0(OP2(1))→H0(IY(k+1)) are of maximal rank. This, together with the maximality of the Hilbert function, gives the graded Betti numbers for the ideal
A note on plane rational curves and associated Poncelet surfaces.
Full text linkAbstract. We consider the parametrization (f_0; f_1; f_2) of a plane rational
curve C, and we want to relate the splitting type of C (i.e. the second Betti
numbers of the ideal (f0; f1; f2) in K[P1] ) with the singularities of the associ-
ated Poncelet surface in P3. We are able of doing this for Ascenzi curves, thus
generalizing a result in [ISV] in the case of plane curves. Moreover we prove
that if the Poncelet surfaces S in P3 is singular then it is associated to a curve
C which possesses a point of multiplicity at least 3
Singularities of plane rational curves via projections
Full text linkWe consider the parameterization f=(f0:f1:f2)of a plane rational curve C of degree n, and we study the singularities of C via such parameterization. We use the projection from the rational normal curve Cn⊂Pn to C and its interplay with the secant varieties to Cn. In particular, we define via f certain 0-dimensional schemes Xk⊂Pk, 2≤k≤(n−1), which encode all information on the singularities of multiplicity ≥k of C (e.g. using X2 we can give a criterion to determine whether C is a cuspidal curve or has only ordinary singularities). We give a series of algorithms which allow one to obtain information about the singularities from such schemes
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
The Use of Videos in the Training of Math Teachers: Formative Assessment in Math Teaching and Learning
Full text linkThe purpose of this chapter is to present a systematic observational research on the math teachers’ assessment practices in the classroom. This research is a specific phase of an international project (FAMT&L - Comenius Multilateral Project) and it is aimed to promote the use of formative assessment in teaching mathematics to students aged from 11 to 16. The observational study is carried out by a plan of systematic observations of teachers’ behaviour in the classroom with the help of video recording. Thanks to a specific tool of video analysis (a structured grid), developed using indications from international literature and experiences of teacher training in the five Partner countries involved (Italy, France, Holland, Switzerland and Cyprus), we managed to gather many different indicators on good and bad practices for the formative assessment of mathematics teachers. Furthermore, the analysed video will be used in in-service teacher training courses in order to promote a correct use of formative assessment and to improve achievements in learning mathematics
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