Math 361, Spring 2013, Assignment 6
From cartan.math.umb.edu
We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.
- - Volatire
Carefully define the following terms, then give one example and one non-example of each:[edit]
- Constructible number.
Carefully state the following theorems (you need not prove them):[edit]
- Theorem characterizing constructible numbers (Theorem 32.6 in the next; note also Corollary 32.8).
- Theorem on the impossibility of certain constructions (Theorems 32.9, 32.10, and 32.11 in the text).
Solve the following problems:[edit]
- Section 32, problems 1 and 3.
