Course Description
- Introduction to Geometry, PMath 360, covers elementary
properties of two non-Euclidean geometries, the real projective plane
and the real hyperbolic plane.
The real projective plane with homogeneous coordinates
is introduced as as an extension of the real Euclidean plane with
with Cartesian coordinates.
Topics include duality, cross ratio, harmonic
conjugates, conics and their poles and polars; also
included are the theorems of Pappus, Desargues, and Pascal.
Other models of the real projective plane are given and finite
projective planes are introduced, including
the smallest finite projective plane, called the Fano plane.
The construction of the real hyperbolic plane is based
on results that arise from the study of inversion with respect
to a circle in the plane.
Stereographic projection gives us
insights into inversion in the plane,
as well as a deeper understanding of
imaginary circles in the real plane.
and is applied to give a simple proof
of the bundle theorem.
Inversion in three space also helps to
better understand stereographic projection and
poles and polars in three space.
Instructor
- Professor
Dickey often keeps hours in DC 2126 on Wednesday
and Friday at 12:30 and on Monday, Wednesday, and some Fridays at 14:30.
He
is also available many other times during the week. Ask for an
appointment or drop in. To find a time convenient for both of
you, it may
be helpful to look at his schedule
which suggests some other possible times.
Email
- Professor Dickey may be reached by e-mail at LJDickey@Math.UWaterloo.CA,
Mention of the
secret password
(the course number) in the the subject line of
your e-mail to
get it through
the spam filters. He may also be reached during office hours in DC
2126, or, (whenever he is around), by phone at 888-4567, extension
35557. Voicemail is not recommended.
Course Notes
- A set of notes called Non-Euclidean Geometry: Course Notes
for PMath 360 by Leroy J. Dickey is
available for purchase from Graphic Services.
This is the third edition. The price is well under $20.
There are some older editions floating around, but this edition has
improvments and additions suggested by last year's users.
Lab
- There is a optional one hour Lab held every Wednesday.
The assignments for which these labs provide assistence
are not optional.
Some students are scheduled for 15:30 and other for
16:30.
The recommended software is GoeGebra which is available at
no cost from GeoGebra.org. It is the only geometry package
presently known that allows the export of PDF (portable document files)
or SVG (scalable vector graphics) images. This may decrease the
pain of pixelation in publications. Assignments may be done
before, during or after lab. There are some other courses that
may be scheduled in the lab from time to time, but there are many open
times when you are also permitted to use the lab. The professor often
attends the Lab, but the presence of a lab assistant is not guaranteed.
Assignments
- The assignments are
available on-line.
Assignment Due Dates
- The assignments are due before the lecture on the Friday
following the Lab.
There will be a drop boxes for this course near
room MC 4066 (the Tutorial Centre) on the fourth floor of the
Math and Computer building.
In recent years we have had boxes 7 or 8,
and slots 11 or 11 or 12. Please put your paper in
the box and slot that is marked for the course.
You might have to get down on your hands and knees to
read the labels.
Put your paper in the appropriately labelled slot!
One year papers that were in the wrong slot made their way
to our hands us months later.
The plan is that the marked papers will be returned to you the
following Wednesday, during the optional Lab or later, in class.
Evaluation
- Weekly assignments will count for 10% of your mark.
There will be n+1 assignments (n yet to be
determined).
The best n-1 of the first n, together with the last, will determine
the homework component of your mark.
Two midterm tests will each count for 15% of your mark. The
dates will be announced in advance.
The final exam will count for 60% of your mark.
This will be at a date and time
scheduled and annnounced by the registrar.
Normally, a passing mark for the homework and for the final
exam are required to earn a passing mark in the course.
There may be an optional final bonus assignment that
you may use to boost the homework component of your mark.
More about this will appear in the
announcements.
Announcements
- Watch for announcements that
will be made from time to time.