Short+Presentations

= **Task:** = Create a presentation on one of the mathematics topics below. //**Use what class time you have well**//. Since we are pressed for class time due to finals and group 4, you will make your presentation as a short powerpoint (around 5 slides) on your netbook. Record your vocal presentation and give Mr. Hurst your file on a portable drive ( I am easy to find). //**Alternatively you may write a 600 word response to one topic and upload to turnitin.**//

= TOK Hand: =
 * You may work individually or in pairs.
 * Topics one through three below, have been covered in class or in the text readings.
 * Topic four was covered by Mr. Andre and is presented in the Radiolab broadcast that has been provided for you.
 * = Assignment is due to me Friday 6/8 =

=__ Choice of Topics __= =__** 1. Riemannian vs. Euclidian geometry **__=

** You might consider some of the following: **

 * Why they were Euclid’s axioms so powerful for 2000 years.
 * What did George Riemann do to/with geometry?
 * Is Riemannian geometry more a practical or abstract tool? Consider that Einstein's Theory of Relativity suggests that space is curved.
 * What if any, are the implications for the nature of mathematical reasoning as a way of knowing and Mathematics as an Area of Knowledge?

=__** 2. Mathematics and Art **__=

**You might consider some of the following:**

 * How are maths and Art related?
 * Examine the works of M.C. Escher
 * Examine the “creation” of fractals
 * To what extent is Mathematics an abstract, creative art?
 * How is Mathematics used to create art?

=__** 3. Kurt Gödeland the ‘Incompleteness Theorem’ **__=

**You might consider some of the following:**

 * What exactly did Gödel do? Explain clearly
 * Can we still be certain about Mathematics
 * Is mathematics still the “science of rigorous proof”?
 * Can we still depend on Mathematics?

=__** 4. Benford’s Law **__=

**You might consider some of the following:**

 * What is it? How did this come about?
 * Is this discovered? Invented?
 * What are the implications about the nature of our world?
 * Do you think the Benford’s Law should exist?
 * To what extent can we know things that are not intuitive?
 * Is this the same as a scientific law?