Euclid and Descartes: A Partnership

1991 ◽  
Vol 84 (9) ◽  
pp. 706-709
Author(s):  
Dorothy Hoy Wasdovich
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
And Algebra ◽  
First Time ◽  
Coordinate Geometry

Although Descartes developed the application of algebra to geometry over 400 years ago, his work has had little impact on the high school geometry course. Geometry and algebra are still taught as separate, unrelated subjects rather than as complementary approaches to mathematics. Any coordinate geometry that is included in a course in Euclidean geometry is apt to be placed in one chapter or unit with the implication that it is “optional” and the material covers theorems that have already been proved. If methods of proof are to be compared, why not do it the first time a theorem is encountered?

The Forum: What Should Become of the High School Geometry Course?: The Present Year-Long Course in Euclidean Geometry Must Go

1972 ◽  
Vol 65 (2) ◽  
pp. 102-154
Author(s):  
Howard F. Fehr
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Mathematics ◽  
Study Group ◽  
High School Geometry ◽  
School Year ◽  
School Geometry ◽  
Long Course ◽  
Coordinate Geometry

It is assumed that the geometey course refers to one that is commonly taught in the tenth school year. It is traditional Euclidean synthetic geometry, 2- and 3-space, modified by an introduction of ruler and protractor axioms into the usual synthetic axioms. A unit of coordinate geometry of the plane is usually appended. It is a course that is reflected in textbooks prepared by the School Mathematics Study Group and in most commercial textbooks.

Fixed Point Theorems in Euclidean Geometry

1973 ◽  
Vol 66 (4) ◽  
pp. 324-330
Author(s):  
Stanley R. Clemens
Keyword(s):  
High School ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Euclidean Geometry ◽  
Transformation Theory ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Points Of View ◽  
Modern Mathematics

The direction of future high school geometry courses is currently the subject of much discussion. One frequent suggestion is that high school geometry should be presented with transformation theory as the unifying theme. In support of this new direction, we shall illustrate that transformations can be employed to bring theorems from classical synthetic geometry into the so-called mainstream of modern mathematics. The thread tying these two points of view together will be the application of fixed point theorems.

Experimental Programs: Coordinate Geometry with an Affine Approach

1964 ◽  
Vol 57 (6) ◽  
pp. 404-405
Author(s):  
Harry Sitomer
Keyword(s):  
High School ◽  
High School Teachers ◽  
School Mathematics ◽  
Study Group ◽  
School Teachers ◽  
High School Geometry ◽  
School Geometry ◽  
Coordinate Geometry

In the spring of 1961, the School Mathematics Study Group convened a group of college mathematicians and high school teachers of mathematics to consider plans for writing an alternate high school geometry course, in which coordinates would be introduced and used as early as feasible.

Neutral and Non-Euclidean Geometry— A High School Course

1977 ◽  
Vol 70 (4) ◽  
pp. 310-314
Author(s):  
Peter A. Krauss ◽  
Steven L. Okolica
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry

Report of a promising classroom-tested alternative in high school geometry.

The Triangles of Aristarchus

2004 ◽  
Vol 97 (4) ◽  
pp. 228-231
Author(s):  
Alan W. Hirshfeld
Keyword(s):  
High School ◽  
Elementary Geometry ◽  
Lunar Eclipse ◽  
Ancient Greek ◽  
High School Geometry ◽  
The Earth ◽  
School Geometry ◽  
Greek Mathematician ◽  
Similar Triangles ◽  
First Time

The ancient Greek mathematician Aristarchus demonstrated for the first time how it was possible, using simple observations and elementary geometry, to measure distances to bodies in the solar system. Aristarchus' methods used a lunar elcipse to approximate the diameter of the Earth, and used the shadow cone of a lunar eclipse to form similar triangles and proportional measurements. The mathmatics can be easily understood by a high school geometry student.

The Lessons Non-Euclidean Geometry Can Teach

1940 ◽  
Vol 33 (2) ◽  
pp. 73-79
Author(s):  
Kenneth B. Henderson
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
Real Difference ◽  
Seventh Grade ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry ◽  
Plane Passing ◽  
Length Width ◽  
Better Than

So YOU want to teach mathematics! Why you selected college geometry is more than I know because college geometry is about as useless as high school geometry. Seriously now, did the fact that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles ever make any real difference in your behavior? And were you thrilled to find out that a line is tangent to a circle if it is perpendicular to the radius drawn to the point of contact? Let me warn you in advance t hat when you find out a line is perpendicular to a plane if it is perpendicular to all lines in the plane passing through its foot, you will be apathetic. Furthermore, when you prove that the volume of a rectangular solid is really the product of the length, width, and height you will probably be disgusted, for you knew t hat ever since you were in the seventh grade. The fact that you proved it is really silly, isn't it? You have gotten along pretty well so far just taking somebody's, a teacher's or author's, word for it. And after all, what difference does it make whether you assume this is so in the first place or whether you assume something else, and from this prove the theorem for finding this volume. None of you would try to make me believe that you can calculate the area of the floor of this room better than Fred Fable whose schedule conflicts prevented him from being one of your classmates in geometry in high school.

For a better mathematics program 2) In high-school geometry

1956 ◽  
Vol 49 (2) ◽  
pp. 100-111
Author(s):  
F. Lynwood Wren
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Teacher ◽  
High School Teacher ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Program

Euclidean geometry is now under attack from well-informed centers. “What should be done about it?” is a very real question for the high-school teacher.

Introduction to non-Euclidean Geometry

1964 ◽  
Vol 57 (7) ◽  
pp. 457-461
Author(s):  
Wesley W. Maiers
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry

A teacher of high school geometry describes a successful unit that convinces pupils that what we prove depends on what we assume.

What are Perpendicular Lines?

1967 ◽  
Vol 60 (1) ◽  
pp. 24-30
Author(s):  
C. R. Wylie
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Mathematics ◽  
Experimental Program ◽  
Study Group ◽  
Recent Issue ◽  
High School Geometry ◽  
School Geometry ◽  
Coordinate Geometry

In a recent issue of The Mathematics Teacher,1 Harry Sitomer described an experimental program in high school geometry originally recommended to the School Mathematics Study Group by some of its advisers but finally undertaken by the Wesleyan Coordinate Geometry Group.

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