Central Philippines State University: Modern Geometry

CENTRAL PHILIPPINES STATE UNIVERSITY CAUAYAN, NEGROS OCCIDENTAL MA 209 Modern Geometry INSTRUCTOR: MICHAEL B. DORONILA, LPT, MAEd

2nd Semester, A.Y. 2021-2022

College of Education COURSE GUIDE I. Course Title:

Modern Geometry

Course Description: The course is an enrichment of the course on Euclidean Geometry. It discusses the properties and applications of other types of geometries such as finite geometry, nonEuclidean geometry and projective geometry. II. Course Overview: A. Introduction This course provides an overview of the field of geometry by studying selected geometries in depth, both Euclidean and non-Euclidean. Inductive exploration and the axiomatic method, as well as synthetic and algebraic approaches to problems, are emphasized. It is the purpose of this course to help overcome this deficiency and to acquaint the student with the concepts and spirit of modern geometries.

B. Course Learning Outcomes At the end of the course, the students would be able to: 1. Understand the key axioms of Euclidean geometry and its associated constructions and theorems. 2. Communicate clearly the foundational concepts of non-Euclidean geometries and their associated constructions and theorems. 3. Apply problem-solving strategies confidently to reach viable solutions of real-world problems II. Course Content: MODULE 1: Axiomatic Method 1. Axiomatic systems 2. Finite geometries

3. Consistency completeness 4. Independence in an axiomatic system

MODULE 2: Foundations of Euclidean geometry 1. A critique of Euclid’s elements

2. A modern set of axioms for Euclidean geometry

MODULE 3: The role of parallel postulate 1. Absolute geometry 2. The Euclidean parallel postulate

3. Discovery on non-Euclidean geometries

MODULE 4: Hyperbolic and other non-Euclidean geometries 1. The Hyperbolic parallel postulate 3. Poincare’s model 2. Some theorems of Hyperbolic geometry 4. Ecliptic geometries MODULE 5: Advanced topics in Euclidean geometry 1. Circles and theory of inversions 2. Verification of Poincare’s model MODULE 6: Introduction to projective geometry

III. Grading System: Midterm/Final Exams 30% Performance Tasks: 70% Worksheets 30% Quizzes 20% Outputs/Projects/ Recitations (face-to-face) 20%________ Total 100%

Prepared By:

MICHAEL B. DORONILA LPT, MAED MA 209 Instructor