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4-colour theorem
 
A brief history and description of the 4-colour theorem and its proof.
A Northern Light Circle Problem
 
In this note Gregory describes a problem involving Dasher and Dancer moving around a Northern Light Circle.
A Rise over Run, and a 10 versus 1
 
A diamond slope, or the slope of the angle bisector, is considered in this note as a generalization of two well-known slope relationships. This general approach is compared then with well-known approaches using various examples.
Aboriginal resources in mathematics education
 
Karen designed this website to assist teachers and pre-service teachers in the area of mathematics from Kindergarten to Grade 12 . Here you will find a multitude of teacher resources to assist you in incorporating Aboriginal content in your mathematics program.
Allison's Star Balls
 
This resource contains instructions on building a uniform polyhedra "star ball" from modules of folded paper. Animation is used to illustrate the folding of the paper. Students are then challenged to construct other uniform polyhedra from the same modules and to discover how they can be "coloured" by using coloured paper. The construction should be possible for beginning middle year students and some of the questions challenging to students at the upper secondary level.
An Arc Midpoint Computation Lesson
 
In this note the authors give an expression for locating the midpoint of a circular arc and a calculator for determining the midpoint.
An Arc Midpoint Computation Proof
 
In this note the authors give an proof of the expression for locating the midpoint of a circular arc that was given in his note with Gregory V. Akulov.
Angles and Polygons: Mathematics 10 (HTML or PDF)
 
Some main concepts discussed in this Stewart Resource unit are properties of polygons, Pythagorean Theorem and Trionometric Ratios. There are five main sections each with corresponding activities. Activites include sections on Objectives, Background Knowledge, Time frame,Iinstructional Methods, Aadaptive Dimension and Assessment.
Approximating pi.
 
This note is a response to a question sent to Quandaries and Queries by Ben Dixon asking how to approximate pi. Chris wrote a nice description of the method used by Archimedes in approximately 250 BC.
Arc Midpoint Algorithm
 
Gregory and Oleksandr have built on the arc midpoint resource and the proof of the arc midpoint formula by constructing an algorithm for finding the coordinates of the midpoint. It is hoped that teachers of high school Mathematics and Computer Science will use these resources to enrich the teaching and learning in both subject areas.
Deriving the Slopes of the Angle Bisectors
 
In this note Gregory uses a trig identity to develop an expression for the slopes of the angle bisectors of two lines in terms of the slopes of the lines that form the angle.
Euclid's proof of the Theorem of Pythagoras
 
This note is a response to a question sent to Quandaries and Queries by Sean Smith asking which of the many proofs of the Theorem of Pythagoras is due to Euclid.
Frieze Designs in Indigenous Art
 
In this article Judi and Harley illustrate the seven frieze patterns using art of the indigenous peoples of North America. They then develope some of the mathematics of frieze patterns at a level that is accessible to many students. The teacher notes contain activities with frieze patterns for students at all levels.
Friezing at Washington State University
 
This article is part of the Mathematics Notes series at Washington State University. In the article, Judi and Harley start by determining the functions that map the plane back onto itself, while at the same time, mapping a specified line back onto itself and preserving the size and shape of any objects represented in the plane. These are the functions that preserve frieze patterns. The authors then look at the algebraic structure of this collection of functions under the operation of composition, show that there are only seven frieze groups, and illustrate how they are generated. Each frieze group is represented algebraically and geometrically. The article concludes with a tour of the Washington State University campus, looking at the ways in which frieze groups are exhibited and used in our immediate surroundings.
Get Into Line (HTML or PDF)
 
This Stewart Resource unit covers many topics some of which are basics of graphing, linear equations, characteristics of a line, arithmetic sequences and series and more. Seven sub-units with lessons are presented with objectives, evaluation ideas and procedures for each.
 
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