This note covers the following
topics: The classical theorem of Ceva, Ceva, Menelaus and Selftransversality,
The general transversality theorem, The theorems of Hoehn and Pratt-Kasapi,
Circular products of ratios involving circles, Circle transversality theorems, A
basic lemma and some applications, Affinely Regular Polygons, Linear
transformations; smoothing vectors, Affine-Regular Components, The general
Napoleon's Theorem, The iteration of smoothing operations.
This course will show how geometry and geometric ideas are a part of
everyone’s life and experiences whether in the classroom, home, or workplace. In
the first chapter of the course notes will cover a variety of geometric topics.
The four subsequent chapters cover the topics of Euclidean Geometry,
Non-Euclidean Geometry, Transformations, and Inversion. However, the goal is not
only to study some interesting topics and results, but to also give “proof” as
to why the results are valid.
In this little treatise
on the Geometry of the Triangle are presented some of the more important
researches on the subject which have been undertaken during the last thirty
years. The author ventures to express not merely his hope, but his confident
expectation, that these novel and interesting theorems some British, but the
greater part derived from French and German sources will widen the outlook of
our mathematical instructors and lend new vigour to their teaching.
This is a course note on Euclidean and
non-Euclidean geometries with emphasis on (i) the contrast between the
traditional and modern approaches to geometry, and (ii) the history and role of
the parallel postulate. This course will be useful to students who want to teach
and use Euclidean geometry, to students who want to learn more about the history
of geometry, and to students who want an introduction to non-Euclidean