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.

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.

Lines as “Foci” for Conic Sections

2019 ◽  
Vol 112 (4) ◽  
pp. 312-316
Author(s):  
Wayne Nirode
Keyword(s):  
Spherical Geometry ◽  
Geometric Object ◽  
Plane Geometry ◽  
Conic Sections ◽  
Geometric Objects ◽  
Definition Of ◽  
Taxicab Geometry

One of my goals, as a geometry teacher, is for my students to develop a deep and flexible understanding of the written definition of a geometric object and the corresponding prototypical diagram. Providing students with opportunities to explore analogous problems is an ideal way to help foster this understanding. Two ways to do this is either to change the surface from a plane to a sphere or change the metric from Pythagorean distance to taxicab distance (where distance is defined as the sum of the horizontal and vertical components between two points). Using a different surface or metric can have dramatic effects on the appearance of geometric objects. For example, in spherical geometry, triangles that are impossible in plane geometry (such as triangles with three right or three obtuse angles) are now possible. In taxicab geometry, a circle now looks like a Euclidean square that has been rotated 45 degrees.

The Case for General Mathematics

1922 ◽  
Vol 15 (7) ◽  
pp. 381-391
Author(s):  
William David Reeve
Keyword(s):  
High School ◽  
Scientific Data ◽  
Plane Geometry ◽  
First Year ◽  
Traditional Methods ◽  
Traditional Practice ◽  
The Third ◽  
Teaching Algebra ◽  
Second Year ◽  
Made In

I shall not attempt, in this paper, to discredit our traditional methods of teaching algebra in the first year of the high school, followed by plane geometry in the second year, intermediate algebra in the third year, and so on. I say this in spite of the fact that much of our traditional practice and the accompanying results might justify one in so doing. In short, I am not interested in a destructive type of criticism of past methods with a view to setting up new bits of content (or at least reorganized content) and technique of procedure. Certainly, I should not favor a method which would seem to be attempting to force any set program upon the teaching body. The best progress is not made in that way. With many teachers of mathematics, the traditional order of treatment, if not the traditional methods, will prevail. Moreover, this will he true even after much experience and available scientific data may make a trial of some form of reorganized content and methods seem wise and feasible.

scholarly journals XXXVI. Properties of the conic sections; deduced by a compendious method. Being a work of the late William Jones, Esq; F. R. S. which he formerly communicated to Mr. John Robertson, Libr. R. S. who now addresses it to the Reverend Nevil Maskelyne, F. R. S. Astronomer Royal.

1773 ◽  
Vol 63 ◽  
pp. 340-360
Keyword(s):  
Plane Geometry ◽  
Conic Sections ◽  
Nevil Maskelyne

Sir, You well know that the curves formed by the sections of a cone, and therefore called Conic Sections, have, from the earliest ages of geometry, engaged the attention of mathematicians, on account of their extensive utility in the solution of many problems, which were incapable of being constructed by an possible combination of right lines and circles, the magnitudes used in plane geometry.

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.

Tips for Beginners: An Impromptu Discovery Lesson in Algebra

1964 ◽  
Vol 57 (6) ◽  
pp. 415-416
Author(s):  
Henry D. Snyder
Keyword(s):  
Lesson Plan ◽  
Quadratic Functions ◽  
Class Session ◽  
Quadratic Equations ◽  
Quadratic Inequalities ◽  
Second Year ◽  
Algebra Class

In a study of quadratic equations and quadratic functions, my second-year algebra class embarked on a discovery lesson which turned out to be the most successful class session I have ever had. The lesson plan called for a consideration of quadratic inequalities and their solutions, but we began as usual by discussing the homework of the previous day.

Parabolic Sound Reflectors–History and Modeling

2019 ◽  
Vol 112 (5) ◽  
pp. 330-337
Author(s):  
Elaine M. Purvinis ◽  
Joshua B. Fagan
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Teachers ◽  
Real Life ◽  
Conceptual Basis ◽  
Time Intervals ◽  
Mathematical Concepts ◽  
Quadratic Equations ◽  
Novel Approach ◽  
Life Challenges ◽  
Second Year

In first- and second-year algebra classrooms, the all-too-familiar whine of “when are we ever going to use this in real life?” challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect to time, and typical lessons include uninspiring textbook practice problems that portray dropping or shooting objects from given distances or at particular time intervals. For a novel approach to exploring quadratics, we chose to step outside the classroom to look at some phenomena in the field of acoustics. Our activity incorporates mathematical modeling to provide a multirepresentational view of the math behind the physics and to provide a conceptual basis for analyzing and understanding a real-world quadratic situation.

Hassles Continue in Second Year Of Medicare Drug Benefit

2007 ◽  
Vol 38 (6) ◽  
pp. 80
Author(s):  
MARY ELLEN SCHNEIDER
Keyword(s):  
Drug Benefit ◽  
Second Year
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