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A Northern Light Circle Problem
 
In this note Gregory describes a problem involving Dasher and Dancer moving around a Northern Light Circle.
A Trig Exercise Inspired by the Use of a Graphing Calculator. (HTML or PDF)
 
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.
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.
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.
Complex Numbers
 
This note is a response to a teacher's request for an explaination of i squared and the square root of i that would be appropriate for secondary level students.
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.
Diamond Slopes and Speedy Whales via… One Identity
 
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.
Puzzle Brings... Olympic Rings
 
Gregory poses a challenge problem involving the Olympic Rings.
The Arc Midpoint Find
 
Continuing his discussion of circular arc midpoint computation Oleksandr develops an expression for the midpoint of a circular arc in n dimensions.
The art of Hamid Naderi Yeganeh
 
Hamid Naderi Yeganeh is a student of mathematics at University of Qom in Iran. He likes to create beautiful images by basic mathematical concepts.
The Identity Crisis in Trigonometry
 
Rick uses a problem sent to Quandaries and Queries to illustrate the usefulness of proving trigonometric identities.
Towards a Better Understanding of Pi Using the Idea of Limits.
 
Ed describes here an activity that students can undertake to approximate pi. It is adapted from the process used by Archimedes in about 240 BC. Students who work through this activity will improve their understanding of pi.
What are real world applications of trigonometry?
 
Students often ask where they will ever use trigonometry or why they need to study it. This note contains a use of trigonomerty in two areas where its use might be unexpected. One situation involves an artisan who needs the dimensions for a metal sculpture he is constructing and the second a homeowner who is disputing her property assessment.
Why is a circle divided into 360 degrees?
 
Kurtis Kredo sent this question to Quandaries and Queries and we thought the answer Chris gave deserved to be in the Resource Room.
 
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