Have you seen this way of doing multiplication ?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
How good are you at finding the formula for a number pattern ?
Investigate matrix models for complex numbers and quaternions.
Find out how the quaternion function G(v) = qvq^-1 gives a simple
algebraic method for working with rotations in 3-space.
See how 4 dimensional quaternions involve vectors in 3-space and
how the quaternion function F(v) = nvn gives a simple algebraic
method of working with reflections in planes in 3-space.
Simon and Trevor used the Newton Raphson method to solve this,
Trevor using a spreadsheet and Simon a program in C. Andrei used
interval halving and a graphical solution.
Go to last month's problems to see more solutions.
This article gives a proof of the uncountability of the Cantor set.
Sketch the graphs for this implicitly defined family of functions.
Ranging from kindergarten mathematics to the fringe of research
this informal article paints the big picture of number in a non
technical way suitable for primary teachers and older students.