## EMT 668 Computers and Algorithms in Mathematics Education

* WRITE UP 1

Find two linear functions f(x) and g(x) such that their product h(x) = f(x).g(x) is tangent to each of f(x) and g(x) at two distinct points. Discuss and illustrate the method and result.

* WRITE UP 2

Some different ways to examine the solution of quadratic equation

In this paper we explore the use of the computer as a tool to explore the solution of quadratics equations in ways that are only possible when using a computer in contrast to the more typical approach of using the computer to draw a large number of graphs - something that could have been done by hand.

* WRITE UP 3

An exploration of triangles and their various points of concurrency.

This paper is both an exploration into the behaviour of certain points of concurrency and a detailed lesson on concepts such as: Centroid, Circumcenter, Incenter, Orthocenter, the Euler line, Nine point circles, Fermat's point, the Orthic triangle, Napoleon's triangle, the Pedal triangle and Miquel points.

* WRITE UP 4

An introduction to the polar equation r = a + b cos (k t) and its graphs

This paper looks at the graphs of a polar equation and examines it in terms of our knowledge of the same graph in rectangular co-ordinates. Through the effective use of the tools Theorist and Algebra Xpressor we can see the relationships quite easily.

* WRITE UP 5

In search of special numbers.

This paper is a reflection on a process used by the author to find a solution to the following task:

Place four numbers in the first row of a spreadsheet. For each successive row replace the entries by the absolute value of the difference of the entry just above and the entry just to the right in the previous row (in the forth collumn use the absolute value of the difference of the number of the entry just above and the entry in the first collumn in the previous row). Will this process lead to a 0 in all 4 entries for some row? What is the largest number of rows before a zero row is generated?

* FINAL PROJECT

A final project consisting of five questions that explore hyperbolas, writing GSP scripts, the use of computer software to teach maximizing problems, Ceva's theorem and one further free choice problem.