Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

Presents three teaching ideas: (1) investigating patterns in the sum of four numbers in a square array, no two from the same column or row; (2) using three-dimensional coordinates to generate models of three tetrahedra; and (3) applying the K=rs area formula for a triangle to other polygons. (MDH)

Two trigonometry problems are presented. The first compares the graphs of the functions arcsin[sin(x)], arccos[cos(x)], and the identity function f(x)=x. The second, using the law of cosines, demonstrates that the solution of a triangle knowing two sides and the excluded angle is no longer ambiguous. (MDH)

Presents lesson plans for activities to introduce recursive sequences of polygons: golden triangles, regular pentagons, and pentagrams. The resulting number patterns involve Fibonacci sequences. Includes reproducible student worksheets. (MKR)

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)

Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those…

In this note, we recall the convex (or barycentric) coordinates of the points of a closed triangular region. We relate the convex and trilinear coordinates of the interior points of the triangular region. We use the relationship between convex and trilinear coordinates to calculate the convex coordinates of the symmedian point of the triangular…

his is the second volume of a series of textbooks on junior high-school mathematics. Like the first volume, it is organized on the principles that were stated in the preface of Book One. Geometry is the basis of the first part of this course. By actual measurement formulas are developed for finding the areas of triangles, quadrilaterals, and the…

This textbook is a young mathematician's guide to mathematics. The following five parts are presented: (1) Arithmetick, vulgar, and decimal, with all the useful rules; and a general method of extracting the roots of all single powers; (2) Algebra, or arithmetick in species; wherein the method of raising and resolving equations is rendered easie;…