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.

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