Devices for the Mathematics Classroom: Simple paper models of the conic sections

1955 ◽  
Vol 48 (1) ◽  
pp. 42-44
Author(s):  
Ethel Saupe
Keyword(s):  
Mathematics Classroom ◽  
Circular Cone ◽  
Conic Section ◽  
Conic Sections ◽  
Quadratic Equations ◽  
Solid Geometry ◽  
Second Year

In second year algebra courses students are normally introduced to the conic sections by being told that certain curves which may be represented by quadratic equations in two unknowns are, in fact, equations of conic sections. In solid geometry the same students are told that a section of a right circular cone made by a plane is a conic section. Various kinds of models are occasionally employed to illustrate what the conic sections look like in the geometric sense, but ordinarily little effort is made to tie up the fact that a relation exists between the introduction given in algebra and the models presented in solid geometry.

Historically Speaking,—: Johan de Witt's kinematical constructions of the conics

1963 ◽  
Vol 56 (8) ◽  
pp. 632-635
Author(s):  
Joy B. Easton
Keyword(s):  
Plane Geometry ◽  
Conic Sections ◽  
Quadratic Equations ◽  
Second Year

In second-year algebra courses the conic sections are defined as type-quadratic equations and the graphs of the curves plotted. It is difficult at this level to relate these equations to the usual geometric definitions of the curves. There arc, however, a number of little-known locus definitions which lead immediately to the canonical equations through the application of elementary theorems of proportion which should be familiar to students of plane geometry.

Demonstration of Conic Sections and Skew Curves with String Models

1946 ◽  
Vol 39 (6) ◽  
pp. 284-287
Author(s):  
H. von Baravalle
Keyword(s):  
High Schools ◽  
Solid Surface ◽  
String Model ◽  
Conic Section ◽  
Slide Projector ◽  
Conic Sections ◽  
Black Background ◽  
Glass Slides ◽  
String Models

For the demonstration of conic sections in high schools and colleges, we generally use the w ooden model of a cone with detachable parts, showing the four kinds of plane sections, a circle, an ellipse, a parabola, and a hyperbola. The wooden model is naturally limited to fixed positions of the intersecting plane and the conic sections appear as four separate facts. As one of the most stimulating parts of a study of conic sections is the realization of how each one of the four curves changes with the position of the intersecting plane and how one kind of conic section can turn into another, a more flexible medium of demonstration seems desirable. It can be found through applying two changes to the usual demonstrations. The first one is to replace the actual cutting of a solid wooden model by projecting a cut on a larger cone, thus achieving an easy flexibility, as either the projector or the model can be moved during the demonstration. The second change is to replace a solid surface by one formed by strings, which not only makes a larger model considerably lighter, but also allows the conic sections to be seen all around the cone. The alternative to string models, models with transparent surfaces, produce too many disturbing light reflections. Figure 1 shows the string model of a cone and Figure 2 its application in the demonstration of ellipses. The system of parallel ellipses in Figure 2 is produced by parallel light planes which are obtained from an ordinary slide projector with slides showing transparent lines on black background. Instead of glass slides also rectangular pieces of stronger drawing paper can be used into which the lines have been cut. Moving the projector slightly to the side makes the ellipses in Figure 2 go up or down the cone and each ellipse widens or contracts during the motion. If one increases the angle of the planes the form of all the ellipses change until they turn into parabolas and finally hyperbolas.

How ICT Affects the Understanding of Stereometry Among University Students

2018 ◽  
Vol 13 (1) ◽  
pp. 37-49
Author(s):  
Nicholas Zaranis ◽  
George M. Exarchakos
Keyword(s):  
University Students ◽  
Undergraduate Students ◽  
Teaching And Learning ◽  
Control Group ◽  
Teaching Methodology ◽  
Van Hiele ◽  
Solid Geometry ◽  
Study Results ◽  
Second Year ◽  
Van Hiele Model

The purpose of this research is to compare the level of competence in stereometry of the university students taught using the authors' ICT oriented learning method based on the Van Hiele model for stereometry concepts, as opposed to traditional teaching methodology. The study deals with second year undergraduate students form the Department of Civil Engineering at Piraeus University. The sample was divided into two groups. The experimental group consisted of 99 students who were taught about basic concepts of solid geometry with the support of computers based on the Van Hiele model. Also, there were 90 students in the control group which were taught with traditional methodology using a dry erase board. The study results showed that teaching and learning through ICT is an interactive process for second year university students and has a positive effect on learning solid geometry concepts using the background of the Van Hiele model.

Who Should Place College Freshmen in Mathematics?

1969 ◽  
Vol 62 (7) ◽  
pp. 557-559
Author(s):  
Ray Kurtz
Keyword(s):  
High School ◽  
College Freshmen ◽  
First Year ◽  
College And University ◽  
Solid Geometry ◽  
Second Year

The placement of college and university freshmen into the appropriate beginning course in mathematics is growing more and more difficult as each school term arrives. A decade or so ago, placement was considerably less of a problem. Each freshman arrived at college with a rather standard high school background in his chosen field of mathematics. If he were well prepared, he had something like first-year algebra, geometry, second-year algebra, trigonometry, and possibly solid geometry. If he possessed less than these courses, his plight was undesirable, but certainly not disastrous, as he could readily enroll in the makeup courses he needed.

scholarly journals DIAGONALISASI BENTUK KUADRATIK IRISAN KERUCUT

2018 ◽  
Vol 19 (1) ◽  
pp. 83-90
Author(s):  
Yusmet Rizal
Keyword(s):  
Quadratic Form ◽  
Cross Product ◽  
Conic Section ◽  
Conic Sections ◽  
Product Term ◽  
Algebraic Concept ◽  
Cross Product Term

In general, the conic section equation consists of three parts, namely quadratic, cross-product, and linear terms. A conic sections will be easily determined by its shape if it does not contain cross-product term, otherwise it is difficult to determine. Analytically a cone slice is a quadratic form of equation. A concept in linear algebraic discussion can be applied to facilitate the discovery of a shape of a conic section. The process of diagonalization can transform a quadratic form into another form which does not contain crosslinking tribes, ie by diagonalizing the quadrate portion. Hence this paper presents the application of an algebraic concept to find a form of conic sections.

Devices for the Mathematics Classroom: A simple quadrant compasses

1954 ◽  
Vol 47 (7) ◽  
pp. 498-500
Author(s):  
William J. Hazard
Keyword(s):  
Mathematics Classroom ◽  
Spherical Trigonometry ◽  
Solid Geometry

The teacher of spherical trigonometry and solid geometry will find the simple quadrant compasses illustrated in Figure 1 a convenient device for drawing circles on a blackened globe. It is easy to use and makes it possible to obtain results that are more uniform than free-hand drawings.

Applications of Quadratic Equations

1945 ◽  
Vol 38 (3) ◽  
pp. 120-125
Author(s):  
William A. Cordrey
Keyword(s):  
Fourth Century ◽  
Conic Sections ◽  
Quadratic Equations ◽  
The Subject

The advent of quadratic equations antedates the dawn of the Christian era by about two millennia. The study of conics, however, did not get under way until the fourth century prior to the birth of Christ. The first writer on this subject, Menaechmus, used the parabola and hyperbola in duplicating the cube. Several years later Euclid wrote a treatise on conic sections. This work was continued by Apollonius, whose investigations added much to the existing knowdedge of the subject.

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