# 80-110 Nature of Mathematical Reasoning

Spring 2002

Dirk Schlimm

Homework 1

Wednesday, January 16

Due Wednesday, January 23

1. Greek mathematicians and philosophers (4 points)

Find the dates of birth and death of the following mathematicians: Thales, Pythagoras, Plato, Eudoxos, Aristotle, Euclid, Hypatia, Archimedes.

Draw a timeline of these mathematicians.

Write a short entry for each of these people, containing their dates and stating their major achievements.

An excellent place to find the relevant information is the website of the MacTutor History of Mathematics Archive http://www-groups.dcs.st-and.ac.uk/~history/index.html ). There is also a link to it from the course website.

2. How much mathematics do you need? (3 points)

Think about how much mathematics you encounter in your daily life and write a summary.

3. Thales' theorem (3 points)

Write down an argument for Thales' theorem, which says: if a triangle is inscribed in a semi-circle in such a way that the base line of the semi-circle is a side of the triangle, then the triangle has a right angle.

Try to be as precise and clear as possible, and carefully state all assumptions that you are making in your argument.