







A diamond slope, or the slope of the angle bisector, is considered in this note as a generalization of two wellknown slope relationships. This general approach is compared then with wellknown approaches using various examples.

AUTHOR(S): Gregory V. Akulov




An example of a problem in algebra or trigonometry that is motivated by an exercise with a graphing calculator. The graph leads to an exercise with a trigonometric identity.

AUTHOR(S): Rick Seaman




In this note the authors give an expression for locating the midpoint of a circular arc and a calculator for determining the midpoint.

AUTHOR(S): Gregory V. Akulov and Oleksandr (Alex) G. Akulov




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.

AUTHOR(S): Oleksandr (Alex) G. Akulov




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.

AUTHOR(S): Oleksandr G. Akulov and Gregory V. Akulov




Gregory and Oleksandr use their Arc Midpoint Computation approach to solve a problem concerning gravitational potential energy and then challenge the reader to solve the same problem using an alternative approach.

AUTHOR(S): Gregory V. Akulov and Oleksandr G. Akulov




Gregory and Oleksandr extend their arc midpoint computation to determine the midpoint of a section of a sine curve.

AUTHOR(S): Gregory V. Akulov and Oleksandr G. Akulov




Gregory finds another application of his arc midpoint computation, this time to the kinetic energy of an object moving along a semicircle.

AUTHOR(S): Gregory V. Akulov




Oleksandr and Gregory extend interpretations of nonpiecewise identities for
sin^(1)x+ sin^(1)y and cos^(1)x+ cos^(1)y using several Euclidean geometry statements and illustrations.

AUTHOR(S): Oleksandr G. Akulov and Gregory V. Akulov




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.

AUTHOR(S): Gregory V. Akulov




A trigonometric identity is used to develop a formula for the slope of a rhombus diagonal. This expression is then used to find the velocity of a whale.

AUTHOR(S): Gregory V. Akulov and Oleksii V. Akulov




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.

AUTHOR(S): Judi McDonald and Harley Weston




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.

AUTHOR(S): Judith J. McDonald and J. Harley Weston




Gregory and Oleksandr find more compact and efficient ways to express some identities involving arcsine and arccosine that appear in the Handbook of Mathematics. The expression Gregory and Oleksandr found was used to derive their arc midpoint computation.

AUTHOR(S): Gregory V. Akulov and Oleksandr G. Akulov




In this note Gregory uses his Arc Midpoint Computation formula to devise a problem regarding riding a bicycle around the University of Victoria campus.

AUTHOR(S): Gregory V Akulov
