Mathematics 153
Notes from May 15, 2020, lecture session

What was covered:
The remaining material from Unit 7 and the material from Unit 8 up to the subsection on mathematical mapmaking.       
Relevant directory files for Units 7 and 8:
Here is a listing of files from Units 7 and 8 which are related to the May 15 lecture, with comments on their significance.  These links are all clickable   
http://math.ucr.edu/~res/math153-2020/week7/unit07/history07.pdf  This is the main file for the unit and should ultimately be read from beginning to end.  After doing so one should read the cited sections of Burton.
http://math.ucr.edu/~res/math153-2020/week7/unit07/seriesexample.pdf   Proof of an infinite series formula from the notes using methods from first year calculus.  
http://math.ucr.edu/~res/math153-2020/week7/unit08/history08.pdf  This is the main file for the unit and should ultimately be read from beginning to end.  After doing so one should read the cited sections of Burton.
http://math.ucr.edu/~res/math153-2020/week7/unit08/man-with-a-pipe.jpg   A famous Picasso cubist painting which surprisingly has some features in common with artwork from the early Middle Ages.
http://math.ucr.edu/~res/math133-2018/geometrynotes04a.f13.pdf   A mathematical discussion of projective geometry, which provides a mathematical framework for the theory of perspective drawing.  This is included only as background, and no material which is only in this document will be tested.
http://math.ucr.edu/~res/math153-2020/week7/unit08/history08c.pdf   Links to interactive WWW sites on the theory of perspective.   This is only included for reference purposes.
http://math.ucr.edu/~res/math153-2020/week7/unit08/history08d.pdf   A mathematical proof that the perspective images of mutually parallel lines meet at a point on the line of the horizon.  This is included only as background, and no material which is only in this document will be tested.
http://math.ucr.edu/~res/math153-2020/week7/unit08/history08b.pdf   Proof that there is no regular honeycomb decomposition of 3-space into regular polyhedra like the standard decomposition into cubes, in contrast to the existence of regular tilings of the plane by equilateral triangles and hexagons.  This is only included for reference purposes and will not be tested.
http://math.ucr.edu/~res/math153-2020/week7/unit08/ln-2.pdf    The value for the natural logarithm of 2 to 30 decimal places.   This is relevant to the material on the "Rule of 72" which is mentioned in the notes (see also the next item).
http://math.ucr.edu/~res/math153-2020/week7/unit08/compounding.pdf    An explanation why the rules of compound interest suggest that the "Rule of 72" is sometimes a good approximation to determining how long it will take for an investment's value to double.