기하학개론

학수구분: 전공선택

강 의 실: 사4-118

수강대상: 수학과 2년

학 점: 3학점

수업시간: 화2 목2

상담시간:  수시

수업목표: Geometer's Sketchpad의 기본적인 사용법을 익힌 뒤, 유클리드 기하, 해석 기하, 비 유클리드 기하, 사영기하 등을 다룬다. 기하학의 오랜 전통으로부터 오는 역사적 배경과 함께 직관을 이용한 문제풀이 그리고  기하의 응용에 대한 내용도 다룬다. 비 유클리드 기하에 대해서는 Cinderella를 이용하여 확인한다.

수업내용: Geometer's Sketchpad의 manual에서 기초적인 사용법; 유클리드 기하; 해석기하; 비 유클리드 기하; 변환 기하; 대칭관계; 사영기하

수업방법 및 자료제시: Geometer's Sketchpad를 이용하여 강의의 내용을 확인하고, 각 주의 마지막 강의에서는 배운 내용에 대한 문제풀이를 한다.

평가계획: 출 석 : 10점

중간평가 : 40점

기말평가 : 40점

레포트 및 발표 : 10점

총점 100점 만점으로 상대평가한다.

교재 및 부교재:

교 재:

1.
Modern Geometry with Applications, by George A. Jennings, Springer-Verlag

2. The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

부교재:

1. Exploring Geometry with the Geometer's Sketchpad

2. Exploring Conic Sections with the Geometer's Sketchpad

3. Introduction to Geometry, Second Edition, by Coxeter, Wiley

4. Geometry, A Comprehensive Course, by Dan Pedoe, Dover

5. Foundations of Geometry, by David Hilbert, Open Court

6. Geometry I, II, by M. Berger, Springer-Verlag

7. Unsolved Problems in Geometry, by Hallard T. Croft, Kenneth J. Falconer and Ricjard K. Guy, Springer-Verlag

8. Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

9. Geometry by Discovery by David Gay

10. Topics in Geometry by Robert Bix

주별수업계획:

제 1주:

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: Euclidean Space

   제 2교시: Isometrices and Congruence

   제 3교시: Reflections in the Plane, Reflections in Space

 

제 2주:  

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: Translations, Rotations

   제 2교시: Applications and Examples

   제 3교시: Some Key Results of High School Geometry

 

제 3주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: The General Isometry

   제 2교시: Geodesics

   제 3교시: The Six Angles of a Spherical Triangle

 

제 4주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: The Law of Cosines for Sides

   제 2교시: The Dual Spherical Triangle

   제 3교시: The Law of Cosines for Angles

 

제 5주 :

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: The Law of Sines for Spherical Triangles

   제 2교시: The Law of Sines for Spherical Triangles

   제 3교시: Navigation Problems

 

제 6주 :

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: Navigation Problems

   제 2교시: Mapmaking

   제 3교시: Mapmaking

 

제 7주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: 중간고사

   제 2교시: 중간고사

   제 3교시: 중간고사

 

제 8주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries by Thomas Q. Sibley

   제 1교시: Conic Sections

   제 2교시: Conic Sections

   제 3교시: Foci of Ellipses and Hyperbolas

     

제 9주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: The Geometric Viewpoint - A Survey of Geometries

             by Thomas Q. Sibley

   제 1교시: Foci of Ellipses and Hyperbolas

   제 2교시: Eccentricity and Directrix

   제 3교시: Eccentricity and Directrix

 

제 10주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Tangent Lines

   제 2교시: Tangent Lines

   제 3교시: Perspective Drawing, Projective Space

 

제 11주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Perspective Drawing, Projective Space

   제 2교시: Desargues' Theorem

   제 3교시: Cross Ratios

 

제 12주:

     교재: Modern Geometry with Applications, by George A. Jennings

     부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Cross Ratios

   제 2교시: Projections in Coordinates

   제 3교시: Tangents

 

제 13주:

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Tangents

   제 2교시: Dual Curves

   제 3교시: Dual Curves

 

제 14주:

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Space Time

   제 2교시: Galilean Tramsformations

   제 3교시: Lorentz Transformations

 

제 15주:

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: Lorentz Transformations

 

   제 2교시: Minkowski Geometry

   제 3교시: Minkowski Geometry

 

제 16주:

       교재: Modern Geometry with Applications, by George A. Jennings

       부교재: Euclidean and Non-Euclidean Geometry by Patrick J. Ryan

   제 1교시: 기말고사

   제 2교시: 기말고사

   제 3교시: 기말고사