Mathematics 153
Notes from April 13, 2020, lecture session

Important change:
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..  
 Homework files:
There is one file each for Unit 1 and Unit 2:
http://math.ucr.edu/~res/math153-2020/week1/unit01/homework01.pdf
http://math.ucr.edu/~res/math153-2020/week2/unit02/homework02.pdf
 Relevant directory files:
Here is a listing with comments on their significance.  These links are all clickable.
Files for Unit 2.
http://math.ucr.edu/~res/math153-2020/week2/unit02/history02.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/week2/unit02/history02a.pdf          AND 
http://math.ucr.edu/~res/math153-2020/week2/unit02/history02d.pdf   These files contain more information on the lunes studied by Hippocrates of Chios.  The first of these files sets up a definite integral formula for the area, and the second has more general information on lunes.  This material will not appear in quizzes or exams.
http://math.ucr.edu/~res/math153-2020/week2/unit02/bisection.pdf   This file describes the standard method for constructing the bisector of an angle by means of (unmarked) straightedge and (collapsible) compass.  Incidentally, Euclid proved a result showing that a construction with (unmarked) straightedge and (rigid) compass, like those sold in school supply stores, can also be done with (unmarked) straightedge and (collapsible) compass.  Here is a reference:
http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Euclid-Second-Proposition-Math-Intell.pdf
This remark will not be used elsewhere in the course or on quizzes and exams.
http://math.ucr.edu/~res/math153-2020/week2/unit02/history02b.pdf          AND 
http://math.ucr.edu/~res/math153-2020/week2/unit02/history02c.pdf          AND 
http://math.ucr.edu/~res/math153-2020/week2/unit02/history02ca.pdf    These three files discuss the three "impossible" construction problems in classical Greek geometry.  The first file discusses the algebraic reasons why such constructions cannot be done using straightedge and compass.  The material in this file is mainly for reference, for it depends heavily on abstract algebra concepts covered in Math 172, and as such the details will not appear on quizzes or examinations.  The remaining two files give ann example of a reasonable looking attempt to perform an angle trisection by straightedge and compass.   The middle file (02c) describes the attempted construction and relates it to a question in trigonomety, and the last file (02ca) uses methods from diffeential calculus to show that the construction never yields a trisection of a given angle.
http://math.ucr.edu/~res/math153-2020/week0/mathproofs2.pdf   This file was shown in the discussion of Aristotle and logical sylllogisms.  The correct way to use syllogisms is to start with (1) if the hypothesis H is true for something, then the conclusion C is also true for that entity, continuing with (2) the hypothesis H is valid in a specific case, and ending with (3) therefore the conclusion C is true in that case.  The dog's also starts with (1), but then it tries to use the validity of C to conclude the validity of H.  In more formal terms, the dog is confusing (1) with its converse!
File 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.
Historical questions:
More questions of this type will be written up and posted to the course directory.