Math 331 Assignment

January 27, 1999

Discussion

• Synthetic geometry v. Cartesian geometry

• Plane geometry, solid geometry, N-dimensional geometry

• Euclidean v. non-Euclidean geometry

• Other kinds of geometry

• What is the Cartesian plane? (Relatively easy)

• When is the Cartesian plane Euclidean?

• What is the synthetic Euclidean plane? (Relatively hard)

  1. What is the meaning of congruence?

  2. What is the meaning of similarity?

• Is there only one Cartesian plane?

• Is there only one synthetic Euclidean plane?

• Is there only one synthetic plane?

• Synthetic methods can be used to prove facts about Cartesian geometry.

• As appropriate, Cartesian methods can be used to prove facts about synthetic geometry.

Exercises due Friday, January 29.

1. Review the procedures from secondary school geometry for constructions.

2. Given a line segment of length a > 0 and a line segment of unit length, i.e., length 1, construct a line segment of length SQRT{a}.

3. Given line segments of length a, b > 0 and a line segment of unit length, construct line segments of length a/b and ab.