Exercise F1

The Fire Tower

I will refer to the version of the article which you can download from the homepage of this course. In this version the page numbering goes from 38 to 53.

Start by reading the introduction in order to get an idea of the background for the article. After that you should focus on the section Analysis in plan page 46-48. You must understand the mathematical content of this section. Here is a list of relevant problems:

• Explain that a rotation is a linear transformation.
• Explain the concept, standard matrix for a linear transformation.
• Show that the standard matrix for a rotation is as claimed in the article, both the general form with sine and cosine and the specific form.
• Repeat the points above for the scaling transformation.
• Explain why M = SR is the standard matrix for the relevant transformation.
• Explain that generally matrix multiplication is not commutative; but that the two matrices S and R commute. Show that by calculations and explain the geometric meaning of it.
• Explain the logarithmic spiral

You are strongly recommended to write down what you find out, so that you can gradually collect material for a manuscript.