GEOMETRY MATH 333

Click on the link syllabus to obtain the file of the original handouts, including information on the paper.

    Source for acrylic hyperbolic planes: J. Charles Jacobson, Department of Mathematics, Elmira College, Elmira, NY 14901             e-mail: Chjacobson@elmira.edu
    Source for crocheted hyperbolic planes: Henderson, Experiencing Geometry in Euclidean, Spherical and Hyperbolic Spaces, 2nd edition, Prentice Hall 2001, pages 49 to 51.  (Designed by Daina Taimina.)

Errata for the text can be found at the link textbook.

A list of homework assignments can be found at  homework.

       ESSAY 1.   What Is A Straight Line?
Due: Sept. 4, 2007
Intended Audience: Good, interested students in high school.
     Format:  Please write your essay using a word processor with a spell checker.  You can draw in any figures by hand.
     Length:  I think at least two pages are needed and that five pages including pictures would be more than such a student would want to know.
     Background: Euclid’s Elements gives the perplexing definition “A straight line is a line which lies evenly with the points on itself.” (See our text, page 287.)  We will see that modern geometry texts don’t bother to define a (straight) line, even though we have strong intuitions about straight lines. This essay topic is modified from Henderson, Experiencing Geometry on Plane, Sphere, and Hyperbolic Plane, Upper Saddle River, N. J.: Prentice Hall, 2001, pages 2-3.
     Topic: Discuss properties of straight lines, in particular those that distinguish them from curves (non-straight lines).  How can you tell practically and theoretically if a line is straight?  In addition to other properties, you may find it helpful to discuss symmetries¹ of lines.  Do your best to define a straight line.
     ¹A symmetry of a figure is a motion that makes the figure coincide with itself overall, even if individual parts of it move around.  For example, a vertical mirror reflection is a symmetry of the letter T, but not of the letter E, which has instead a horizontal mirror reflection as a symmetry.  There are several other types of symmetry as well, such as rotations and translations.     

     ESSAY 2.   Axiomatic Systems and Models
Due: Sept. 18, 2007
Intended Audience: Good, interested students who have finished Calculus II.
     Format:  Please write your essay using a word processor with a spell checker.  You can draw in any figures by hand (or use photocopies with acknowledgment).
     Length:  I think at least two typed pages are needed to cover the topic and that five pages would be more than such a student would want to know.
     Topic:  Explain what an axiomatic system and a model are and why they are important to mathematicians.  Illustrate with examples appropriate and interesting to your audience.  You should address some of the metamathematical ideas, but there is no need to discuss all of them, especially given your audience.  You do not need to give technical definitions if you feel your audience would better understand your essay with only informal descriptions and examples.

There are many web sites of interest in geometry.  Probably the best place to start looking for these (and other mathematical web sites) is at the Forum and in particular its library of web sites.  Click  http://forum.swarthmore.edu to go to the Forum.  By adding   /library  you will get to its library.

    Fr. Magnus Wenninger, a St. John's monk and retired mathematics teacher, has a web site devoted to polyhedra.   Two of the display cases in the Peter Engel Science Center feature a few of his polyhedra.  He would be happy to meet will anyone interested in poyhedra.   Send him e-mail at mwenninger@csbsju.edu or call him at extension 3885.