For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates,…

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for the author, 3-D geometry is the branch of mathematics that shows…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…

In this article, framed as a conversation, the authors discuss the learning resulting from a variety of geometry tasks they have conducted with their students. None of them are convinced that all the geometry tasks within the numeracy strategy prescribed in English schools are necessarily good for children or aimed at the right age range. Using…

The ancient Greek mathematicians sought to construct, by use of straight edge and compass only, all regular polygons. They had no difficulty with regular polygons having 3, 4, 5 and 6 sides, but the 7-sided heptagon eluded all their attempts. In this article, the authors discuss some cosine relations and the regular heptagon. (Contains 1 figure.)

This guide contains an outline of topics to be included in individual subject areas in secondary school mathematics and some specific suggestions for teaching them. Areas covered include--(1) fundamentals of mathematics included in seventh and eighth grades and general mathematics in the high school, (2) algebra concepts for courses one and two,…

In the first of these two lessons, students study the concepts of three sides of equal length, three equal angles, plane figure, closed figure, and simple figure by reading descriptions, considering examples and nonexamples, and completing exercises. On the second day they combine these concepts in a definition of equilateral triangle. The…

Pascal's triangle can be used as early as grades five and six to teach children to recognize mathematical patterns. Children can be guided to discover patterns or sequences of numbers if they begin with pictures or physical objects which they can manipulate and count. (Author/BB)

The cube is the most familiar and in many ways the simplest of the five regular polyhedra, and yet it is surprisingly rich mathematically. This article suggests a number of practical activities for the classroom which involve the cube and related polyhedra. (PK)

Patterns of equilateral triangles, squares, rectangles, and regular pentagons are provided for students to use in building models of polyhedra. (DT)

Provides an activity to develop students' (grade 5 through 10) spatial understanding and problem solving ability. Describes materials, prerequisites, directions, extensions, and technology using Geometric Supposer software. Presents worksheets and answers. Four references are listed. (YP)

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

Provides a method of demonstrating triangles on a curved surface to aid the student in seeing that the sum of the angles are either more or less than 180 degrees depending upon which side of the sphere the triangle is placed. (MVL)

An activity designed as an introduction to High School geometry empowering students to see relationships and make geometric connections. A list of student generated relationships based on student constructed and manipulated diagrams is included. Discussion guidelines are suggested. (DE)