A method is given for the analysis of geodesic domes involving plane geometry. The method shows how to calculate all necessary angles and chords, given the length of one side. (MP)

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Gives definitions of taxicab geometry and the MacDraw format for graphing. In the world of taxicab geometry, movement through the plane is along horizontal and vertical paths. Describes specific application to conic sections, including circle, ellipse, parabola, and hyperbola. Lists five references. (YP)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

Discusses some theorems and properties of figures produced when circles are tangent to one another. (GA)

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)

Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

Discusses Napoleon's involvement with mathematics and education. Describes two geometric constructions dividing the circumference of a circle into four equal parts and finding the center of a given circle. Summarizes the establishment of the Institute of Egypt and the educational system in France. Twenty-seven references are listed. (YP)

Discussed are two Euclidean constructions (synthetic approach and coordinate method) to inscribe regular polygons of 5 and 17 sides in a circle. Each step of the constructions is described using diagrams and mathematical expressions. (YP)