Axiomatic Geometry - Mathematics 360 -
Spring 2009
For Homework 9
- In the proof of the theorem on page 41, it says we can apply a rotation
and then a translation so that p ends up on the y-axis, and q and r on the
x-axis. Give a Euclidean transformation in terms of arbitrary complex
numbers p, q, and r that does this.
- In the first full paragraph on page 44, it says "In this position,
the midpoints ... are easily calculated." How would the
midpoints be calculated in an arbitrary position? Give formulas in terms
of p, q, and r.
- Now review your solutions to problems 5-7 on page 47; can you simplify
any of them?