The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

This article describes how a series of lessons might be used to allow students to discover the size of the Earth, the distance to the Moon, the size of the Moon, and the altitude of Mount Piton on the Moon. Measurement with a sextant, principles of geometry and trigonometry, and historically important scientists and mathematicians are discussed.

Suggests an alternative proof by analytic methods, which is more accessible than rigorous proof based on Euclid's Elements, in which students need only apply standard methods of trigonometry to the data without introducing new points or lines. (KHR)

Presents proofs of some trigonometric identities from a geometric point of view. (MKR)

Describes an analysis of the direction taken by a baseball immediately after coming into contact with the bat. Uses geometry, trigonometry, and physics. (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

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…

Introduces handling data as conceived by Euclid, which provides some interesting possibilities for students to investigate fundamental geometrical ideas as well as relating some elementary geometry with elementary trigonometry. (ASK)

Students can learn to make algebra, trigonometry, and geometry work for them by using matrices to rotate figures on the graphics screen of a graphing calculator. Includes a software program, TRNSFORM, for the TI-81 graphing calculator which can draw and rotate a triangle. (MKR)

This course syllabus is for five 18-week courses in the Metal Fabrication Program at Northeast Wisconsin Technical College (NWTC): (1) metal fabrication I; (2) blueprint reading and sketching; (3) applied layout tech I; (4) metal fabrication II; and (5) applied layout tech II. Each syllabus contains some or all of the following: (1) course…

Presented are activities and references involving tangrams. Seven pieces are cut from a single square of paper; other shapes and objects are made from these pieces. (RH)

Describes a method of effectively introducing the concept of radian measure that uses Cabri Geometry II software to construct a circle of arbitrary radius and to measure that radius. The goal is to determine how many of these radii fit around a circle. (DDR)

Demonstrates the use of hexagonal dot paper in integrating algebra, geometry, and trigonometry within a single problem-solving setting rather than treating them in isolation. Suggests other related mathematically challenging activities for enrichment. (AIM)

Includes two activities: (1) a skit to review variations of the trigonometric functions, and (2) a geometry problem about maximizing costs that exposes students to a variety of different solution strategies and makes the material more meaningful. (MKR)

Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)