Chapter 6 Alternative Concepts for Parallelism: NonEuclidean Geometry
6.1
6.2
6.3
6.3
Historical Background of Non-Euclidean Geometry
An Improbable Logical Case
Hyperbolic Geometry: Angle Sum Theorem
Hyperbolic Geometry Enrichment and Workbook
Homework 7
Chapter 4 Euclidean Geometry
4.1 Euclidean Parallelism, Existence of Rectangles
4.2 Parallelism and Trapezoids: Parallel Projection
4.3 Similar Triangles, Pythagorean Theorem,
Trigonometry
4.5 The Circle Theorems
Homework 6
1
4.1 Euclidean Parallelism, Ex
3.3 Spherical Geometry
Neutral Geometry (axioms below) is a structure that works for all of the Big Three
geometries: Euclidean, Spherical, and Hyperbolic. You just make certain choices
about the distance boundary and the situation about parallel lines an
3.1
3.2
3.3
Triangles, Congruence Relations, SAS Hypothesis
Taxicab Geometry: Geometry without SAS Congruence
SAS, ASA, SSS Congruence, and Perpendicular Bisectors
Absolute Geometry
We are building axioms that will result in one of two choices*: Euclidean
2.1 An Introduction to Axiomatics and Proof
2.2 The Role of Examples and Models
2.3 Incidence Axioms for Geometry
Homework assignment 1
1
2.1
An Introduction to Axiomatics and Proof
An axiomatic system is a formalized construct that is used in business, r
Math 5397 - 03
Summer 2010
Instructor:
Email:
Website:
Leigh Hollyer
dog@uh.edu
www.math.uh.edu/~dog
Textbook:
College Geometry: a Discovery Approach, second edition
David C. Kay
ISBN 0-321-04624-2
Chatroom:
Testing:
link on my website
must be proctored.
MATH 5397 HW4
Things that are the same in Euclidian geometry and Spherical Geometry
1.
Both systems are axiomatic in nature
2.
Both systems share the 16 neutral geometry axioms
3.
Both systems include polygons with 3 or more sides (Triangles, Quadrilatera
Homework 7
6.2
2, 8
Enrichment exercise: Do the Moment for Discovery in Absolute Geometry on page 433
Be sure to write it up nicely with illustrations and complete answers. Feel free to
check with any other student in the class to make sure youve got
it.
Homework assignment 3
3.1 3.2 8, 12 1, 2, 3, 4, 6, 9, 13 & 15
Enrichment: In Euclidean Geometry, circles have 3 possible relationships: they don't intersect at all they intersect in one point they can be internally tangent or externally tangent they inter
Hint for the final.
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
15 points
15 points
10 points
15 points
15 points
30 points
Angle sum of triangles new proof
Summary of EG, HG, and SG essay
Matching 10 statements with 8 situations
A n
1. Define corrosion
Corrosion is the degradation of a metallic element, it converts from a pure form into a nonmetallic compound.
2. Answer the following
a. Distinguish between oxidation and reduction
i. Oxidation: Refers to an element giving away electro