Professor: Jeff Johannes
Section 1 MWF 12:30-1:20p
Office Hours: Monday 2:30 - 3:30p, Wednesday 8 - 9p,
Thursday 11:30a - 12:30p and 2 - 3p, Friday 2:30 - 3:30p, and by appointment
Email Address: Johannes@Geneseo.edu
Experiencing Geometry: Euclidean and
Non-Euclidean with History (Third Edition), David W. Henderson and
To develop a deep and personal understanding of
Euclidean, spherical and hyperbolic geometries and how they relate to
measuring the universe in which we live.
This course will take a more philosophical perspective on
geometry rather than a computational or result-based perspective. In
this class we will use several different methods to analyse
geometries. We will rarely have traditional lectures. More
frequently will be times for individual work, group work, and class
discussion. While there will be some familiar looking homework
exercises, there will mostly be more personal discussions of homework
I have intentionally chosen Henderson‚€™s book as an
exploratory and philosophical text. In addition to planning time to do
homework, please take time to carefully read the chapters in the book.
Notice use of the words ‚€œtime‚€ and ‚€œcarefully‚€. Read the
sections slowly. Read actively, that is while writing and with models
at hand. If you do not understand some statement reread it, think of
some potential meanings and see if they are consistent, and if all else
fails, ask me. If you do not believe a statement, check it with your
own examples. Finally, if you understand and believe the statements,
consider how you would convince someone else that they are true, in other
words, how would you prove them?
Upon successful completion of Math 335 a student will be
‚€Ę Compare and contrast the geometries of
the Euclidean and hyperbolic planes.
‚€Ę Analyze axioms for the Euclidean
and hyperbolic planes and their consequences.
‚€Ę Use transformational and axiomatic
techniques to prove theorems.
‚€Ę Analyze the different consequences
and meanings of parallelism on the Euclidean and hyperbolic planes.
‚€Ę Demonstrate knowledge of the
historical development of Euclidean and non-Euclidean geometries.
Your grade in this course will be based upon your
performance on two styles of homework, a project, an in-class exam and a
final experience. The weight assigned to each is designated below:
Homework Problems 3/5
Throughout the course you will write up discussions of
‚€œProblems‚€ from Henderson‚€™s book. Before these papers are handed
in, I strongly suggest somehow submitting drafts to me for comments.
These drafts are not required, but will strengthen your understanding and
your final products. Drafts can either be submitted in paper or via
email. Either way I will return them with comments and
suggestions. The end goal of writing each problem will be presenting
your complete understanding of the question in a well-written
discussion. These discussions will be graded on a ten point decile
scale based on completeness, accuracy and writing.
These problems will be evaluated similarly to evaluating
papers in an English class.
0 missing or plagiarised
3 question copied, nothing written
6 something written that appears that it was only written
to take up space
7 substantially incomplete. Something written, but
does not really answer the main questions. Major errors.
Very poor writing
8 mostly complete. maybe a few minor errors
9 complete, no errors, some personal insight,
10 wonderful (includes concise, and to the the
Solutions and Plagiarism
There are plenty of places that one can find all kinds of
solutions to problems in this class. Reading them and not referencing
them in your work is plagiarism, and will be reported as an academic
integrity violation. Reading them and referencing them is not quite
plagiarism, but does undermine the intent of the problems. Therefore,
if you reference solutions you will receive 0 points, but you will *not* be
reported for an academic integrity. Simply ‚€¶ please do not read any
solutions for problems in this class.
Each student is responsible for completing a project as
part of a pair. A project will consist of reading one of chapters
11,14-22 from Henderson‚€™s book or a similar portion of another book not
discussed in class (I have several options you may examine). The
materials for the projects must be chosen by February 22. Each project
will include a write-up of all the problems in the chosen part.
Finally, each of the projects will be presented in the last two weeks of
The final experience will include extensive writing and
focused on summarizing the experience of different aspects of the
course. This product will be due at the time of the scheduled
final exam, May 12, 12-3p, when we will also meet to discuss the topic and
the course as a whole.
We may occasionally using Geometer‚€™s Sketchpad as a
method of gaining intuition for geometry. Details for working with
this software will be described in class.
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for how the
course is running. Remember, the sooner you tell me your concerns, the
more I can do about them. I have also created a web-site
accepts anonymous comments. If we have not yet discussed this in
class, please encourage me to create a class code. This site may also
be accessed via our course page on a link
feedback. Of course, you are always welcome to approach me
outside of class to discuss these issues as well.
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning disabilities.
Students should consult with the Director in the Office of Disability
Services (Tabitha Buggie-Hunt, 105D Erwin, firstname.lastname@example.org) and their
individual faculty regarding any needed accommodations as early as possible
in the semester.
It is my policy to give students who miss class because
of observance of religious holidays the opportunity to make up missed
work. You are responsible for notifying me no later than February 4 of
plans to observe the holiday.
January 25 ‚€“ February 13 Discuss Chapters
1-5 of Henderson
As a homework exercise,
show a model of a hyperbolic plane
February 18 - March 10 Discuss
Chapters 6, 7, 9 of Henderson
up of Chapters 1-5 ‚€œProblems‚€ due
must be chosen by this date.
March 11 - 29
8, 10 of Henderson
Drafts of Chapters 6, 7, 9 will not be accepted after
Final write up of Chapters 6, 7, 9 ‚€œProblems‚€ due
April 1 ‚€“ 18
Discuss Chapters 11, 12 of
Henderson, and Constructions
Drafts of Chapters 8, 10 will not be
Final write up of Chapters 8, 10 ‚€œProblems‚€ due
Drafts of Chapters 12, 13 will not be accepted
April 26 ‚€“ May 6
Written projects due. Final write up of
Chapters 12, 13 "Problems" due
Wednesday May 15, 12-3p Final
experience - leftover presentations.