Mathematics 153
Notes from April 15, 2020, lecture session

Reminder:
Due to storage capacity issues, the recordings of lectures have been moved to the course directory.  The first lecture in this series is
 http://math.ucr.edu/~res/math153-2020/April06.mp4 
and the names for subsequent lectures are indicated by their dates.
 What was covered:
The first part of Unit 3, up to but not indcluding the subheading Limitations of the Elements.  
 Homework files:
There is one file for Unit 3:
http://math.ucr.edu/~res/math153-2020/week1/unit01/homework03.pdf
 Relevant directory files:
Here is a listing with comments on their significance.  These links are all clickable.
Files for Unit 3.
http://math.ucr.edu/~res/math153-2020/week3/unit03/history03.pdf   This is the main file for the unit and should be read from beginning to end.  After doing so one should read the cited sections of Burton.
http://math.ucr.edu/~res/math153-2020/week3/unit03/elements-toc.pdf   A chart summarize the contents of Euclid's Elements.  There are three parts; the first six books cover plane geometry, the next four cover properties of numbers, and the final three cover solid geometry through the description of the five regular polyhedra.
http://math.ucr.edu/~res/math153-2020/week3/unit03/hinge-theorem.pdf   This proves the theorem stated in the title and applies it to derive the final propositions in the second book of the Elements.  
http://math.ucr.edu/~res/math153-2020/week3/unit03/quadcirc.pdf   Drawing of a convex quadrilateral which can be inscribed in one circle and has another circle inscribed inside it.
http://math.ucr.edu/~res/math153-2020/week3/unit03/eudoxus.pdf   A summary of the basic properties of rational numbers needed to derive the Condition of Eudoxus.  
http://math.ucr.edu/~res/math153-2020/week3/unit03/history03a.pdf   Algebraic details involving the condition of Eudoxus and its meaning for ratios which are not rational numbers.
http://math.ucr.edu/~res/math153-2020/week3/unit03/history03b.pdf   The proof of the proportionality theorem for triangles when the ratio is not a rational number.
http://math.ucr.edu/~res/math153-2020/week3/unit03/prime-proof.pdf   Euclid's proof that there are infinitely many primes, coupled with some comments about a common misconception of what it proves and what it does not prove.
Homework:
See http://math.ucr.edu/~res/math153-2020/week3/unit03/homework03.pdf. 
Quiz 1:
This will be a take-home quiz and will be posted Tuesday, April 21.