Day 4

Math 444, Wednesday, 10/5
Sponsor Today's class is brought to you by the Triangle Inequality and other fine inequalities everywhere.
Topics Definitions of vertical angles, exterior angle. Inequalties about triangle angles and sides. Triangle inequality. Perpendicular bisector as a boundary of Voronoi diagrams.
Class Schedule
  • Definitions of vertical angles; prove vertical angles are equal.
  • Definition of exterior angle of a triangle ABC. Prove exterior angle at A is greater than interior angles at B or C.
  • Prove: (Bigger side-bigger angle) In triangle ABC, angle A > angle B iff BC > CA.
  • LOGIC point. Prove iff by contrapositive and cases.
  • Prove: Triangle inequality.
  • Corollary: The perpendicular bisector of AB divides the plane into 2 regions called half-planes. One is the set of points closer to A than B and one is the set of points closer to B than A.
  • Def: Voronoi diagram (or Dirichlet domains or region). Given a set of points A, B, C, ..., divide up the plane into regions. The region for one of the given points P is the set of points closer to P than any of the other points in the given set.
  • .Further connections: Reflection in a line, light reflection in a mirror, paper folding.
Assignments
New

Reading Assignment (due Friday 10/7)

Read BB, constructions, pp. 172-174 (through angle bisection), p. 181-183, 185-187.

Voronoi reading on e-reserve!

Notes on inequalities on e-reserve!.

Assignment 3 (due Wednesday 10/12)

.TBA
Due Today

Assignment 2 due at beginning of class.
Ongoing None

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