# Réponse finale obtenue du bot:
response = « **Course Title:** Geometry and Beyond: Euclidean, Non-Euclidean, Trigonometry, and Topology
**Course Description:** This course is designed to provide a comprehensive overview of geometry, covering both classical Euclidean geometry and modern non-Euclidean geometries, as well as trigonometry and topology. Students will learn the fundamental principles and concepts of each field, and develop problem-solving skills through hands-on exercises and projects.
**Course Outline:**
**Week 1-2:** Introduction to Geometry
* Overview of geometric shapes and their properties
* Euclidean geometry: points, lines, planes, angles, and measurements
* Basic trigonometry: angles, triangles, and functions
**Week 3-4:** Euclidean Geometry
* Properties of congruent and similar figures
* Theorems of similarity and congruence
* Applications to real-world problems (e.g., architecture, engineering)
**Week 5-6:** Non-Euclidean Geometries
* Introduction to non-Euclidean geometries: hyperbolic and elliptical
* Key concepts: curvature, angles, and measurements
* Comparison of Euclidean and non-Euclidean geometries
**Week 7-8:** Trigonometry
* Advanced trigonometric functions: inverse trig functions and identities
* Applications to real-world problems (e.g., navigation, physics)
* Trigonometric equations and identities
**Week 9-10:** Topology
* Introduction to topological spaces and their properties
* Fundamental groups and homotopy
* Applications to real-world problems (e.g., graph theory, computer science)
**Week 11-12:** Final Project and Review
* Students will work on a final project that applies geometric concepts to a chosen problem or topic
* Review of key concepts and formulas throughout the course
**Assessment:**
* Quizzes and exams (40%)
* Homework assignments and projects (30%)
* Class participation and attendance (10%)
* Final project presentation (20%)
**Prerequisites:** None, but some background in mathematics is recommended.
**Target Audience:** Students interested in geometry, trigonometry, and topology, as well as those seeking a comprehensive introduction to these fields.
**Course Materials:**
* Textbook: « Geometry: Seeing, Doing, Understanding » by Harold R. Jacobs
* Online resources: Khan Academy, MIT OpenCourseWare, etc.
* Calculators and graphing software (optional)
**Instructor:** [Your Name], Ph.D., Mathematics Department
**Office Hours:** [List your office hours]
I hope this course outline helps! Let me know if you have any questions or need further clarification. »