Mathematics and Human Nature

Use 2 full pages to answer to the following questions.

Book: Cheng, E. (2015). How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

Questions for Chapter 5 and 6:
1. Is generalization always allowed and correct in mathematics? What examples does Cheng provide?

2. How is Taxicab Geometry a “generalization”? Describe at least three other mathematical generalizations cited by Cheng and make sure you state how and why they are mathematical generalizations.

3. According to Cheng, what does it mean for mathematical activity to be internally motivated and what does it mean for mathematical activity to be externally motivated? Give an example of each (used by Cheng).

4. What is “proof by contradiction”? How would I prove by contradiction that it is not raining?