Course in Hyperbolic Geometry
2014
Page updated 23.3.2014
News
(updated 8.3.2014)
On Thursday 12th of April Eric Lehman
makes a short repetition on what was done in February 2012 course, and
goes on with one more Chapter of Spherical and projective geometry.
From Friday on we concentrate on
creating Geometry on sphere workshop for SciFest2012.
Please make your suggestion of the
times which suit you, if you will take part in the teaching and/or SciFest
workshop.
Most important is to do it for
Thursday and Friday, 12th and 13th April. After that we can choose the
time and place more freely.
You can write your suggestion in the GoogleDocs shared document, whose URL address will be emailed to you soon.
Tentative time-table for the teaching
SPHERICAL GEOMETRY
The aim of this course is to show different aspects of spherical geometry
for itself, in relation to applications and in relation to other geometries
and other parts of mathematics.
The chapters will be (mostly) independent from each other.
To begin, we'l work on the sphere as Euclid did in the plane looking
at triangles. Many things look alike, but there are some striking differences.
The second viewpoint will be the introduction of coordinates and the
application to basic astronomy.
The theorem of Pythagoras has a very nice and simple shape in spherical
geometry.
To contemplate spherical trigonometry will give us respect for our
ancestors and navigators, but we shall skip the tedious computations and
let the GPS do them.
The stereographic projection is a marvellous tool to understand the
pencils of coaxial circles and many aspects of
the relation between the spherical geometry, the euclidean affine
plane, the complex projective line, the real projective plane, the
Möbius strip and even the hyperbolic plane.
The course can be taken in three volumes:
1 cp: Active participation in February
12-hour course.
2 cp: Active participation in February
12-hour course and supplementary written work (exam or essay).
4 cp: Active participation in February
12-hour course and supplementary written work (exam or essay) and active
participation in April 6-hour course 13.-17.4.
Group work: Preparing SciFest2012
workshop dealing with the course material, tutoring the workshop and reporting.
Info: Martti.Pesonen (cat tail) uef.fi