# Number - September 2007, Stage 4&5

## Problems

### Napier's Location Arithmetic

##### Stage: 4 Challenge Level:

Have you seen this way of doing multiplication ?

### Expenses

##### Stage: 4 Challenge Level:

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

### Interactive Number Patterns

##### Stage: 4 Challenge Level:

How good are you at finding the formula for a number pattern ?

### Two and Four Dimensional Numbers

##### Stage: 5 Challenge Level:

Investigate matrix models for complex numbers and quaternions.

### Quaternions and Rotations

##### Stage: 5 Challenge Level:

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

### Quaternions and Reflections

##### Stage: 5 Challenge Level:

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.