How to determine when there is a unique solution when two sides and an angle of a triangle are known, using simple algebra and the law of cosines, is described. (MNS)

Discussed are two approaches to determining which regular polygons, either inscribed within or circumscribed about the unit circle, exhibit rational area or rational perimeter. One approach involves applications of abstract theory from a typical modern algebra course, whereas the other approach employs material from a traditional…

Algebraic and transcendental curves are discussed, with attention focused on computing the area of some special regions bounded by the curves. (MNS)

The given proof supplements the derivation of identities provided in textbooks. Illustrations are included. (MNS)

In this section, suggestions are given for working with radian measures, proving logarithmic properties, the law of cosines as seen by Pythagoras, and an alternative proof of a theorem. (MNS)

Some traditional and some less conventional approaches using the cotangent to solve the same problem are described. (MNS)

The use of paper folding to study properties of geometric solids is discussed. (SD)

Provided is an analysis, using concepts from geometry, algebra, and trigonometry, to explain the apparent loss of area in the rug-cutting puzzle. (MNS)

Examples are given of computer activities in analytic geometry. (MK)

After students learn that it is impossible to trisect an angle using compass and straight-edge, students are introduced to the trisectrix curve which accomplishes the trisection. (SD)

Presents an extension of a Japanese mathematics lesson involving the area of a triangle and introduces concepts from trigonometry. (ASK)

The subject of parallax can motivate learning related to measurement of lengths and angles as well as provide an introduction to trigonometric concepts. (SD)

This module, designed for use at the high school level as a four- to eight-hour topic, includes: the geometry of a sphere, the coordinate system used to describe points on the earth's surface, parallel and meridian sailing, and the solution of right spherical triangles. (Author/MK)

Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)

The geometry of perspective drawing is developed and discussed. (SD)