Homework1
A reminder: you are free to collaborate, but you must understand and write up the final answers by yourself!
Write up your answers on a separte sheet. You do not need to include a cover page, but your name and mailbox must be on the first page. Staple multiple pages.
- Show that the following sequences commute:
- A rotation and a uniform scaling
- Two rotations about the same axis
- Two translations
General proof for any inputs 0: No general cases 1: Any inputs Show single commute permutation 0: No transformations 2: Single way commutes Show commute permutations are equal 0: Single commutativity 2: Show both commutes -
Show that any sequence of rotations and translations can be replaced by a single rotation about the origin followed by a translation.
Prove basic finite R T cases 0: No transform cases 4: Proves basic cases Prove basic infinite R T cases 0: No transform cases 4: Proves infinite cases Prove complex infinite R T cases 0: No infinite cases 5: Proves infinite cases General proof for any inputs 0: No general cases 2: Any inputs -
Three vertices determine a triangle if they do not lie in the same line. Devise a test for collinearity of three vertices.
Collinear test method 0: No method 3: Algorithm without justification 6: Algorithm by example 8: Justified algorithm Correct algorithm 0: Does not work at all 2: Correct for many inputs 5: Correct for all inputs General proof for any inputs 0: No general cases 2: Any inputs