Exercise F2

The Fire Tower

This exercise covers the part of the article starting with the section Analysis of the front elevation page 48 and ending on page 49 line 8 from below, that is ending with but not including the section beginning with "Four conic spirals". This is the last part of the article which you should concentrate on.

Here is a list of relevant problems:

• Explain that a translation is not a linear transformation and explain how this problem is overcome using homogeneous coordinates.
• Explain why the matrices R^*, S^*, T₁^* and M₁^* actually "do the job" rotation, scaling, translation and "all in one" respectively.
• Examine both geometrically and by calculations whether some of the matrices R^*, S^* and T₁^* commute.
• Explain the formula for the height of the 12 cubes.