Hyperbolic Geometry
1
Hyperbolic Geometry
Johann Bolyai
Karl Gauss
Nicolai Lobachevsky
18021860
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Note. Since the rst 28 postulates of Euclids Elements do not use the
Parallel Postulate, then these results will also be valid in our rst exa
Math 420 - Homework 3
September 11, 2012
These questions do not come from the textbook. I may be posting some relevant material on
the class website for your consumption.
1
Stretching
The parallel postulate states that: if a straight line falling on two s
Math 420 - Homework 4
October 2, 2012
1
Coin Flip
We will often study hyperbolic geometry in the Poincar disk. The following questions discuss
e
properties of that object.
1. Often we will use the unit circle |z | < 1 for z C to dene the Poincar disk. Obv
Math 420 - Homework 2
September 4, 2012
This homework will constitute most of our coverage of Chapter 2 in the book. You will be
expected to read through the book to answer these questions. This homework, unlike the previous
one, will be graded and I expe
Math 420 - Homework 2
September 4, 2012
This homework will constitute most of our coverage of Chapter 2 in the book. You will be
expected to read through the book to answer these questions. This homework, unlike the previous
one, will be graded and I expe
Math 420 - Homework 1
August 28, 2012
This rst homework is designed to be rather gentle, and to get you acclimated to the way we
work problems here. These problems can be found in various places throughout the book (Ill try
to point out where). Please typ
Math 420 - Homework 5
October 16, 2012
1
Batting Practice
This section deals with a couple proofs from some of our earlier material. It is assigned here to
provide additional practice with proofs. As such, I expect these proofs to be complete, well though
Math 420 - Homework 6
November 6, 2012
1
Heavy bag
Examine the image in Figure 1, which is constructed after being given triangle ABC .
Figure 1: This triangle and associated constructs were created in GeoGebra.
1. Recreate this picture in GeoGebra using
4. Hyperbolic Geometry
4.1 The three geometries
Here we will look at the basic ideas of hyperbolic geometry including the ideas of lines,
distance, angle, angle sum, area and the isometry group and nally the construction
of Schwartz triangles. We develop
Exploration of Spherical Geometry
Michael Bolin
September 9, 2003
Abstract. We explore how geometry on a sphere compares to traditional plane geometry. We
present formulas and theorems about the 2-gon and the 3-gon in spherical geometry. We end
with an al