If an object is conveniently located in front of two plane mirrors placed at an angle, an observer can see a superposition of images that results in a face with three eyes, called in this text a "triclops." The conditions of occurrence of such an image may seem trivial, but this is incorrect: rather, the correct interpretation of this…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

The Department of Mathematics and Statistics at Utah State University offers two courses for preservice secondary school mathematics teachers that complement each other in working toward a vision for school mathematics in which "all students have access to high-quality, engaging mathematics instruction." Through these courses, students…

Reports a proof of a classical geometry problem. The proposition is - In any triangle there are two equal sides, if the angles opposite these sides have angle bisectors with equal lengths. (RP)

This article shows how simple instruments may be used to construct angles of certain measures and applies this procedure to more detailed problems. A proof of the Pythagorean Theorem is given using these procedures. (CT)

This book, photographically reproduced from its original 1942 edition, is an extended essay on one of the three problems of the ancients. The first chapter reduces the problem of trisecting an angle to the solution of a cubic equation, shows that straightedge and compasses constructions can only give lengths of a certain form, and then proves that…

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)

At Kings River Community College, analyses were conducted of the grades and characteristics of students in Mathematics A (Elementary Algebra), Mathematics B (Plane Geometry), Mathematics C (Trigonometry), and Mathematics D (Intermediate Algebra) to determine which variables were significantly related to student success. Data were gathered on 69…

This program guide presents civil engineering technology curriculum for technical institutes in Georgia. The general information section contains the following: purpose and objectives; program description, including admissions, typical job titles, and accreditation and certification; and curriculum model, including standard curriculum sequence and…