Last time: More on Irrational
numbers. Reusing or extending perfectly good proofs.
...an irrational number...lies hidden in a kind of cloud of infinity. -- Michael Stifel
Today:
Hand back homework. Observations:
Many of you focussed on simply describing what is already
in the book: I wanted you to delve deeper, and try to
explain how the strategy works!
Some of you did not realize that the "official homework"
was on the web, and didn't address question #3. I
didn't "count off" for this.
It was good to use an example, in gory detail.
There were lots of unsubstantiated assertions, e.g. "every
non-Fibonacci number can be written as a sum of
non-consecutive Fibonacci numbers."
No one contacted me for any help! The best way is to email
me at longa@nku.edu.
Next time: not as gentle! Make sure you show me your
effort, creativity, and, most of all, mathematical
care!
Homework Assignment #2: For next Friday, fix assignment 1!
Specifically here is assignment 2. Hand in your
assignment 1 with assignment 2! I want to see improvement, of
course!
Project Assignment 1 due: let me know whether you're going it
alone, or with another today.
Project Assignment 2 (due 10/4): let me know what your topic is,
and some preliminary details about what your poster will
cover.
Project idea: Soap bubbles and minimal surfaces.
Get out your 3-D glasses! Have a look at the figure on p. 126.
Why does every interval on the real line contain an infinite
number of rational numbers?
Why does every interval on the real line contain an infinite
number of irrational numbers?
What is the argument given for the fact that there are more
irrationals than rationals?