MATH3050.06 First Week
Since I will ask you to give your 'geometry
autobiography', I have posted by own geometric autobiography for you amusement! I hope it gives
you some small insight into my own questions and
a slice of my own 'mathematical life'.
Assignment 1. Due September 13
Write a short (roughly 2-5 page) 'geometry autobiography', including items such as:
* Remember, such questions are required in every assignment! You must
include them in this assignment.
- What has been your previous exposure to formal geometry
(as in high school courses, summer jobs, applications to
other fields etc.)
- What has been your previous exposure to informal geometry:
(origami, sewing, carpentry etc.), sports, observing nature, design?
- Why geometry is taught in high school?
- * What are a couple of key questions you would like to
to during this year of geometry (including possible questions about
learning, about 'proving', about visual thinking,
about the history of the subject, about
Explorations at the First Class
We will begin with Section 1 of the text: Experiencing Geometry on Plane and Sphere, by David Henderson. This will include a number of small group explorations on `What is a straight line?' I will provide some spheres, cones, paper and ribbons
to use in these explorations.
We will work on this in the first class. Make some notes
to bring to at the second class and
I will ask you to discuss your
ideas in small groups. After this discussion and whatever
questions you have in the second class, I will ask you to begin
to write up your response to Problems 1 and 2 in the text.
We will have some additional time to discuss your ideas
and questions - and the assignment is due September 25.
I will hand out a problem on "bicycle tracks". This is actually
directly related to the idea of what it looks like and feels like
to turn - and to the idea that straight means not turning.
- Here are a couple of web pages related to `straight' and
'curving' paths (courtesy of Eli Brettler):
- Some text for the bicycle
Some sample tracks to apply the exercise on
Remember, these tracks either fit a bicycle moving forward
up the page or down the page (but not both).
Which is it? Can you prove your answer is correct?
- What is the connection between this exercise and
the question `What is a straight line'? You can discuss
this within Assignment 2 (below).
- I have now posted some
hints on analysing the
Assignment 2. Due September 25
Write your solutions to Problems 1 and 2 in Henderson.
In writing this, you should make use of:
The written response will be individual, but you are encouraged
to discuss your answers with other students inside and
outside of class.
- what was discussed in class, either as a whole group or as
in small groups;
- suggestions in the book;
- your own experiences and examples (including the
bicycle track exercise above);
- some connections between straight lines and symmetry.
* Remember to include your
questions on every assignment. These may be directly
related related to the assignment; a continuation of a dialog begun in the first
assignment; or questions provoked by experiences outside the course.
Such questions / dialog are required in the assignment.
The class is not full. If you know other students who are interested
in the course, they should get in touch with me immediately.
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