So we decided to call “straight line” (…): Mathematics students’ interaction and negotiation of meaning in constructing a model of elliptic geometry

Used by mathematicians over two thousand years ago, the compass and straightedge are still used by mathematics students today. The straightedge is similar to the ruler in that the user can draw a straight line with it, but the straightedge is not marked and cannot be used to measure things. Although many different types of compasses exist, your students probably use the modern compass. The characteristic that makes the modern compass special is tension, which allows the opening between the lead and the pointer to be fixed. By fixing the opening, the user can draw a circle of a given radius and copy a line segment.

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Metrical Coordinates in Non-Euclidean Geometry

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500013742 ◽

1932 ◽

Vol 3 (1) ◽

pp. 16-25

Author(s):

D. M. Y. Sommerville

Keyword(s):

Euclidean Geometry ◽

Plane Geometry ◽

Non Euclidean Geometry ◽

Straight Line ◽

Elliptic Geometry ◽

Space Constant

§1. The coordinates considered are linear, i.e. in a plane the equation of a straight line, and in space the equation of a plane, is linear in the coordinates. We shall first consider point-coordinates in plane geometry, taking elliptic geometry as typical, with space-constant unity.

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MEMINIMALKAN KESULITAN BELAJAR PESERTA DIDIK DENGAN PENDEKATAN KONSTRUKTIVIS

Vidya Karya ◽

10.20527/jvk.v34i1.6401 ◽

2019 ◽

Vol 34 (1) ◽

pp. 47

Author(s):

Dormauli Simanullang

Keyword(s):

Learning Outcomes ◽

Mathematics Learning ◽

Student Response ◽

Constructivist Approach ◽

Mathematics Students ◽

Student Responses ◽

Student Activities ◽

Straight Line ◽

Learning Mathematics ◽

Class Viii

Abstract. This study aims to minimize the difficulty of learning mathematics students by applying learning with a constructivist approach. This classroom action research was conducted on class VIII students of SMP PGRI 3 Banjarmasin, which amounted to 30 people, for 3 cycles. Data collection was done by test and non-test techniques, using learning outcomes tests, observation sheets, and student response questionnaires. Data were analyzed quantitatively and qualitatively. The results showed that (1) student activity in learning increased to 93%; (2) student responses to learning is fun; and (3) student learning completeness increases to 97%. Thus, it can be concluded that mathematics learning with a constructivist approach is able to minimize the difficulty of learning mathematics students on the topic straight line equations. Keywords: constructivist approach, learning difficulties, student activities, straight line equations. Abstrak. Penelitian ini bertujuan untuk meminimalkan kesulitan belajar matematika siswa dengan menerapkan pembelajaran dengan pendekatan konstruktivis. Penelitian tindakan kelas ini dilaksanakan pada siswa kelas VIII SMP PGRI 3 Banjarmasin yang berjumlah 30 orang, selama 3 siklus. Pengumpulan data dilakukan dengan teknik tes dan non tes, menggunakan tes hasil belajar, lembar pengamatan, dan angket respon siswa. Data dianalisis secara deskriptif kuntitatif dan kualitatif. Hasil penelitian menunjukkan bahwa (1) aktivitas siswa dalam pembelajaran meningkat menjadi 93%; (2) respon siswa terhadap pembelajaran adalah menyenangkan; dan (3) ketuntasan belajar siswa meningkat menjadi 97%. Dengan demikian, dapat disimpulkan bahwa pembelajaran matematika dengan pendekatan konstruktivis mampu meminimalkan kesulitan belajar matematika siswa pada topik persamaan garis lurus. Kata kunci: pendekatan konstruktivis, kesulitan belajar, aktivitas siswa, persamaan garis lurus.

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PENERAPAN PEMBELAJARAN KOOPERATIF NUMBER HEAD TOGETHER (NHT) UNTUK MENINGKATKAN KEMAMPUAN KOMUNIKASI MATEMATIKA SISWA KELAS VIII SMP IT SUHADAH YOGJAKARTA

Prisma Sains Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram ◽

10.33394/j-ps.v2i1.1058 ◽

2014 ◽

Vol 2 (1) ◽

pp. 83

Author(s):

Mariamah Mariamah

Keyword(s):

Cooperative Learning ◽

Communication Skills ◽

Type Number ◽

Mathematics Students ◽

Mathematical Communication ◽

Mathematical Ideas ◽

Student Activity ◽

Test Instrument ◽

Straight Line ◽

Communication Ability

This study aims to determine the ability of communication mathematics students in grade VIII SMP IT Suhadah Yogyakarta through cooperative learning type Number Head Together (NHT). This study is a classroom action research. The instrument used to collect data is a test instrument. The results of the research for the students' communication ability aspects improved from cycle I of cycle II for each aspect: the first aspect is illustrating mathematical ideas from 30% to 47%, an increase of 17%. The second aspect describes the answer and the use of symbols from 20% to 40.5%. The increase is as much as 20.5%. The total achievement for cycle II is 85.7%, which in this case has reached the criteria 85.7%> 85%. We conclude that NHT learning has been effective for students' mathematical communication skills on straight-line equations. In addition, for teacher and student activity, in the first cycle only active categories have increased

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PENGEMBANGAN KOMPETENSI SIKAP DALAM PEMBELAJARAN MATEMATIKA SECARA HOLISTIK BERSUMBER QUR’AN

Jurnal Pendidikan Matematika dan IPA ◽

10.26418/jpmipa.v10i1.30033 ◽

2019 ◽

Vol 10 (1) ◽

pp. 149

Author(s):

Agung Hartoyo ◽

Asep Nursangaji ◽

Dede Suratman

Keyword(s):

Core Competencies ◽

Mathematics Learning ◽

Mathematics Students ◽

Competency Development ◽

Teaching Materials ◽

Mathematical Concepts ◽

Holistic Learning ◽

Straight Line ◽

Knowledge Competencies ◽

Spiritual Attitude

AbstractThis study aims to describe the process of developing spiritual and social attitudes competencies, in a holistic learning of mathematics sourced in the Qur'an. Qualitative research is applied in the preparation of teaching materials based on the integration of core competencies of revised Curriculum-13, and the development of attitude competencies in mathematics learning based on the Qur'anic. The subjects of the study were SMP / MTs students in the lessons of Straight Line Equation. The research data includes documents, learning recordings, and interviews, and it’s analyzed using the Miles & Huberman Method. The study resulted in: (1) mathematics teaching materials on the topic of the Straight Line Equations sourced of the Qur'anic (al Anfal) verses 65-66, to teach holistically, (2) The process of developing competency attitudes is carried out as long as the learning takes place from introduction to closing the lesson. In developing a spiritual attitude, two students are assigned to read the verses of the Qur’an and their translations, then discuss the content of mathematics. Students are aroused by curiosity with questions about verse, working collaboratively with friends, choosing the best ideas (tolerant), and being responsible for completing tasks. In developing skills and knowledge competencies, students are guided to achieve the process of modeling problems related to the Qur'anic verses, so that they find problem solving procedures, or mathematical concepts from the topics studied.Keywords: attitude competency development, holistic mathematics learning.

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Microdensitometer—computer correlation analysis of ultrastructural periodicity

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100081024 ◽

1978 ◽

Vol 36 (2) ◽

pp. 32-33

Author(s):

D.R. Ensor ◽

C.G. Jensen ◽

J.A. Fillery ◽

R.J.K. Baker

Keyword(s):

Correlation Analysis ◽

Background Noise ◽

Computer Control ◽

Optical Diffraction ◽

Screw Thread ◽

Straight Line ◽

Computer Storage ◽

Correlation Process ◽

Electron Microscope Image ◽

Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

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Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100076834 ◽

1983 ◽

Vol 41 ◽

pp. 646-647

Author(s):

Joseph A. Zasadzinski

Keyword(s):

Liquid Crystalline ◽

Freeze Fracture ◽

Continuum Theory ◽

Closed Surfaces ◽

Straight Line ◽

Low Weight ◽

Concentric Spheres ◽

Membrane Geometry ◽

Dupin Cyclides ◽

Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

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Human Enamel Replication

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100090889 ◽

1976 ◽

Vol 34 ◽

pp. 180-181

Author(s):

Norman L. Dockum ◽

John G. Dockum

Keyword(s):

Organic Matrix ◽

Human Teeth ◽

Human Enamel ◽

Straight Line ◽

Ultrastructural Characteristics

Ultrastructural characteristics of fractured human enamel and acid-etched enamel were compared using acetate replicas shadowed with platinum and palladium. Shadowed replications of acid-etched surfaces were also obtained by the same method.Enamel from human teeth has a rod structure within which there are crystals of hydroxyapatite contained within a structureless organic matrix composed of keratin. The rods which run at right angles from the dentino-enamel junction are considered to run in a straight line perpendicular to the perimeter of the enamel, however, in many areas these enamel rods overlap, interlacing and intertwining with one another.

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