scholarly journals Are Points (Necessarily) Unextended?

2022 ◽  
pp. 1-40
Author(s):  
Philip Ehrlich
Keyword(s):  
Euclidean Geometry ◽  
The Given

Abstract Since Euclid defined a point as “that which has no part” it has been widely assumed that points are necessarily unextended. It has also been assumed that this is equivalent to saying that points or, more properly speaking, degenerate segments, have length zero. We challenge these assumptions by providing models of Euclidean geometry where the points are extended despite the fact that the degenerate segments have null lengths, and observe that whereas the extended natures of the points are not recognizable in the given models, they can be recognized and characterized by structures that are suitable expansions of the models.

scholarly journals ON THE ESSENCE, THE PLACE, THE PART AND CHARACTER OF THE TASKS WITH PARAMETERS IN THE GEOMETRY COURSES OF THE INSTITUTIONS OF GENERAL SECONDARY EDUCATION

2020 ◽  
Vol 1 (191) ◽  
pp. 150-154
Author(s):  
Olena Synyukova ◽  
◽  
Oleh Chepok ◽  
Keyword(s):  
Secondary Education ◽  
Euclidean Plane ◽  
Euclidean Geometry ◽  
Axiomatic Theory ◽  
Geometrical Figure ◽  
Long Time ◽  
Mutual Displacement ◽  
The Given ◽  
Independent Assessment ◽  
Parameter Relation

The so-called tasks with parameters for a long time now have become an integral part as of the every to some extent profound course of algebra or of algebra and the beginnings of cultures at the institutions of general secondary education, as of the corresponding tasks of the State Final Attestation in Mathematics and the External independent assessment in mathematics. And it isn’t accidental because in the most often cases the solution of the task with a parameter turns for the student into a small investigation by his own. The realization of such investigation favors the formation of the creative practical-oriented personality. Simultaneously we must state that, despite of the existence of a lot of the high scientific and methodical level created corresponding training books, it is difficult just now to find in the methodical literature the clear answers to the natural questions of what is meant on the whole by the task with parameter (or with parameters) and its solution. At the same time, in the courses of geometry of the institutions of general secondary education to the tasks with parameters it is given next to nothing consideration. But in fact such tasks in the courses are present, their importance for the proper construction of the courses can be exaggerated. In the paper the problems of what must be understand by the task with the parameter or with the parameters and by its solution are analyzed. The essence, the part and the place of the tasks with parameters in the geometry courses of institutions of general secondary education are elucidated. Euclidean geometry as an axiomatic theory investigates the sets that in their overwhelming majority represent by themselves the mathematical abstructions of the spatial forms of the surrounding, some relations between such set and quantities that characterize such sets and relations. In the contrast to the courses of algebra, in the geometrical courses the part of parameters may be played by all of the three mentioned components. Geometrical figures can change by the size and by the form. Changing by the size bring us to the concept of the scalar quantity. Changing by the form are considered in the tasks of paving and, for example, in the tasks of finding the amount and the types of symmetries of geometrical figure in dependence of its form. The part of the parameter-relation can be played by different variants of mutual displacement of the given figures in Euclidean plane or in Euclidean space. According to their content, different geometrical tasks with parameters are considered in the work. The task of the existence of geometrical figures, the tasks, conserning the character of some geometrical places of points, the tasks of tracing with the help of a compass and a ruler are among them.

scholarly journals Elementary Considerations relating to the Absolute

1909 ◽  
Vol 28 ◽  
pp. 65-72
Author(s):  
Duncan M.Y. Sommerville
Keyword(s):  
Fixed Point ◽  
Special Interest ◽  
Euclidean Geometry ◽  
Criterion A ◽  
Parallel Lines ◽  
Non Euclidean Geometry ◽  
The Absolute ◽  
The Given

Non-Euclidean geometry in the narrowest sense is that system of geometry which is usually associated with the names of Lobachevskij and Bolyai, and which arose from the substitution for Euclid's parallel-postulate of a postulate admitting an infinity of lines through a fixed point not intersecting a given line, the two limits between the intersectors and the non-intersectors being called the parallels to the given line through the fixed point. In a wider sense, any system of geometry which denies one or more of the fundamental assumptions upon which Euclid's system is based is a non-euclidean geometry. Of special interest are, however, those which touch only the question of parallel lines ; and there exists, in addition to Lobachevskij's geometry, another, commonly associated with the name of Riemann, in which the parallels to any line through a fixed point are imaginary. The three geometries, Lobachevskij's, Euclid's, and Riemann's, thus form a trio characterised by the existence of real, coincident, or imaginary pairs of parallels through a given point to a given line. With reference to this criterion, a consistent nomenclature was introduced by Klein, who called these three geometries respectively Hyperbolic, Parabolic, and Elliptic.

Franz Kafka's “The Burrow” (“Der Bau”): An Analytical Essay

PMLA ◽  
1972 ◽  
Vol 87 (2) ◽  
pp. 152-166 ◽  
Author(s):  
Hermann J. Weigand
Keyword(s):  
Life Span ◽  
Euclidean Geometry ◽  
Traumatic Experience ◽  
Primary Level ◽  
Non Euclidean Geometry ◽  
Close Analysis ◽  
Symbolic Interpretation ◽  
The Given ◽  
First Time

Previous commentaries have emphasized the correlation between this piece and the host of motifs and problems that Franz Kafka never tired of treating. While this method seems mandatory in an overall account and has led to stimulating insights as well as aberrations on various levels of symbolic interpretation, a close analysis of “The Burrow” on the primary level, granting the given data of its non-Euclidean geometry, is attempted for the first time. Outstanding features include a demonstration of the unique quality of the recital as the synchronous coexistence of a ninety-minute monologue in the form of an emergent or progressive present with a life span of many years extending from maturity to senility. The progressive derangement and deterioration of the hero are analyzed, and his persecution mania is correlated with manifestations of a repressed, abnormal libido that allows inferences regarding a traumatic experience of his youth. Finally, it is shown on inner grounds of both a formal and a material nature that the piece is complete, allowing of no meaningful continuation.

Personal Problem Solving of Partners in Divorce Proceedings

2015 ◽  
Vol 36 (1) ◽  
pp. 82-103 ◽  
Author(s):  
Tereza Soukupova ◽  
Petr Goldmann
Keyword(s):  
Gender Differences ◽  
Problem Solving ◽  
Thematic Apperception Test ◽  
Scoring Systems ◽  
Personal Control ◽  
Personality Characteristics ◽  
Personal Problem ◽  
Thematic Apperception ◽  
And Gender ◽  
The Given

Abstract. The Thematic Apperception Test is one of the most frequently administered apperceptive techniques. Formal scoring systems are helpful in evaluating story responses. TAT stories, made by 20 males and 20 females in the situation of legal divorce proceedings, were coded for detection and comparison of their personal problem solving ability. The evaluating instrument utilized was the Personal Problem Solving System-Revised (PPSS-R) as developed by G. F. Ronan. The results indicate that in relation to card 1, men more often than women saw the cause of the problem as removable. With card 6GF, women were more motivated to resolve the given problem than were men, women had a higher personal control and their stories contained more optimism compared to men’s stories. In relation to card 6BM women, more often than men, used emotions generated from the problem to orient themselves within the problem. With card 13MF, the men’s level of stress was less compared to that of the women, and men were more able to plan within the context of problem-solving. Significant differences in the examined groups were found in those cards which depicted significant gender and parental potentials. The TAT can be used to help identify personality characteristics and gender differences.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

Coordinating Medical Literature with Patient Care

1977 ◽  
Vol 16 (04) ◽  
pp. 234-240 ◽  
Author(s):  
Joann Gustafson ◽  
J. Nelson ◽  
Ann Buller
Keyword(s):  
Health Care ◽  
Medical Staff ◽  
Medical Information ◽  
Medical Literature ◽  
Medical Information System ◽  
Staff Members ◽  
Information Displays ◽  
Medical Displays ◽  
Computerized Medical Information ◽  
The Given

The contribution of a special library project to a computerized problem-oriented medical information system (PROMIS) is discussed. Medical information displays developed by the PROMIS medical staff are accessible to the health care provider via touch screen cathode terminals. Under PROMIS, members of the library project developed two information services, one concerned with the initial building of the medical displays and the other with the updating of this information. Information from 88 medical journals is disseminated to physicians involved in the building of the medical displays. Articles meeting predetermined selection criteria are abstracted and the abstracts are made available by direct selective dissemination or via a problem-oriented abstract file. The updating service involves comparing the information contained in the selected articles with the computerized medical displays on the given topic. Discrepancies are brought to the attention of PROMIS medical staff members who evaluate the information and make appropriate changes in the displays. Thus a feedback loop is maintained which assures the completeness, accuracy, and currency of the computerized medical information. The development of this library project and its interface with the computerized health care system thus attempts to deal with the problems in the generation, validation, dissemination, and application of medical literature.

Identification and Transformation of Terminal Morphemes in Medical English

1969 ◽  
Vol 8 (02) ◽  
pp. 84-90 ◽  
Author(s):  
A. W. Pratt ◽  
M. Pacak
Keyword(s):  
Word Form ◽  
Subsequent Transformation ◽  
Part Of Speech ◽  
Morphological Segmentation ◽  
Medical English ◽  
Nominal Form ◽  
Admissible Path ◽  
Near Future ◽  
The Given ◽  
Admissible Sequences

The system for the identification and subsequent transformation of terminal morphemes in medical English is a part of the information system for processing pathology data which was developed at the National Institutes of Health.The recognition and transformation of terminal morphemes is restricted to classes of adjectivals including the -ING and -ED forms, nominals and homographic adjective/noun forms.The adjective-to-noun and noun-to-noun transforms consist basically of a set of substitutions of adjectival and certain nominal suffixes by a set of suffixes which indicate the corresponding nominal form(s).The adjectival/nominal suffix has a polymorphosyntactic transformational function if it has the property of being transformed into more than one nominalizing suffix (e.g., the adjectival suffix -IC can be substituted by a set of nominalizing suffixes -Ø, -A, -E, -Y, -IS, -IA, -ICS): the adjectival suffix has a monomorphosyntactic transformational property if there is only one admissible transform (e.g., -CIC → -X).The morphological segmentation and the subsequent transformations are based on the following principles:a. The word form is segmented according to the principle of »double consonant cut,« i.e., terminal characters following the last set of double consonants are analyzed and treated as a potential suffix. For practical purposes only such terminal suffixes of a maximum length of four have been analyzed.b. The principle that the largest segment of a word form common to both adjective and noun or to both noun stems is retained as a word base for transformational operations, and the non-identical segment is considered to be a »suffix.«The backward right-to-left character search is initiated by the identification of the terminal grapheme of the given word form and is extended to certain admissible sequences of immediately preceding graphemes.The nodes which represent fixed sequences of graphemes are labeled according to their recognition and/or transformation properties.The tree nodes are divided into two groups:a. productive or activatedb. non-productive or non-activatedThe productive (activated) nodes are sequences of sets of graphemes which possess certain properties, such as the indication about part-of-speech class membership, the transformation properties, or both. The non-productive (non-activated) nodes have the function of connectors, i.e., they specify the admissible path to the productive nodes.The computer program for the identification and transformation of the terminal morphemes is open-ended and is already operational. It will be extended to other sub-fields of medicine in the near future.

The Role and Place of Budget Procedure in the System

2003 ◽  
pp. 42-49 ◽  
Author(s):  
E. Bushmin
Keyword(s):  
Budget Process ◽  
Public Expenditures ◽  
Principal Role ◽  
Process Trends ◽  
The Given ◽  
Rules Of The Game

The article is devoted to the analysis of improving budget process trends. The author offers the concept of "financial technologism". Its usage should promote an essential improvement of the budget process. The given concept is based on the fact that the regulation of budget procedure is the process of determination of "rules of the game", and the order of interaction of different institutions within the framework of the budget process, and the trends and volumes of expenses are the strategy of institutions. The procedure within the budget process plays a principal role as compared with the trends and volumes of public expenditures.

Deskripsi Kesulitan Belajar Siswa Berdasarkan Karakteristik Lerner dalam Menyelesaikan Soal Geometri

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Nazom Murio ◽  
Roseli Theis
Keyword(s):  
Qualitative Research ◽  
Visual Perception ◽  
Learning Difficulties ◽  
Research Subjects ◽  
Visual Objects ◽  
Almost All ◽  
Personality Classification ◽  
The Given ◽  
Classification Test ◽  
Descriptive Qualitative

Geometri adalah bagian matematika yang sangat dekat dari siswa, karena hampir semua objek visual yang ada di sekitar siswa adalah objek geometri, tetapi tidak semua siswa menyukai pembelajaran yang menyertakan gambar, sehingga memungkinkan siswa mengalami kesulitan dalam belajar geometri. Tujuan dari penelitian ini adalah untuk menggambarkan kesulitan belajar siswa berdasarkan karakteristik Lerner dalam menyelesaikan pertanyaan geometri. Jenis penelitian ini adalah penelitian deskriptif kualitatif. Subjek penelitian adalah siswa dengan kepribadian wali yang mengalami kesulitan belajar di kelas IX A SMP N 30 Muaro Jambi. Instrumen yang digunakan dalam penelitian ini adalah penulis sendiri, lembar tes klasifikasi kepribadian, lembar tes kesulitan belajar, dan pedoman wawancara. Hasil penelitian menunjukkan siswa dengan kepribadian wali yang mengalami kesulitan belajar, 100% mengalami kelainan persepsi visual, di mana siswa mengalami kesulitan dalam menentukan seperti apa bangun datar pada masalah tersebut. 60% mengalami kesulitan mengenali dan memahami simbol, di mana siswa melihat simbol "//" sebagai simbol untuk kesesuaian. Serta 40% mengalami kesulitan dalam bahasa dan membaca, di mana siswa kesulitan dalam memahami pertanyaan yang diberikan.   Geometry is a very close mathematical part of the student, because almost all visual objects that exist around the students are objects of geometry, but not all students like learning that includes images, thus allowing students to have difficulty in learning geometry. The purpose of this research is to describe students' learning difficulties based on Lerner's characteristic in solving the geometry question. This type of research is descriptive qualitative research. Research subjects were students with guardian personality who had difficulty studying in class IX A SMP N 30 Muaro Jambi. Instruments used in this study are the authors themselves, personality classification test sheets, learning difficulties test sheets, and interview guidelines. The results showed students with guardian personality who experienced learning difficulties, 100% experienced visual perception abnormalities, where students have difficulty in determining what kind of flat wake on the matter. 60% have difficulty recognizing and understanding symbols, where students see the symbol "//" as a symbol for conformity. As well as 40% have difficulty in language and reading, where students difficulty in understanding the given question.

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