Geometry
Teachers KAMIDE, Norihiro Year 2　I/III [Department of Information Science Correspondence Course, Faculty of Science and Engineering] Basic Major Subjects メディア授業 Elective　2credit 4B207

#### Course Description

Euclidean geometry and projective geometry are explained based on the following theorems: (1) Ceva's theorem, (2) Menelaus' theorem, (3) Pascal's theorem, (4) Brianchon's theorem, and (5) Desargues' theorem. An introduction to analytic geometry (Cartesian geometry) is given based on the following items: (1) conic sections (ellipse, parabola and hyperbola) and (2) quadric surfaces (ellipsoid, hyperboloid of one/two sheet(s), elliptic paraboloid, etc.). Some cutting-edge topics on modern geometry (topology, graph theory, and computational geometry) are introduced.

#### Course Objectives

The aim of this course is to understand the following items: (1) basic theorems in Euclidean geometry and projective geometry, (2) some applications of these basic theorems, (3) basic properties of conic sections, (4) standard forms of conic sections, (5) basic properties of quadric surfaces, and (6) history and types of modern geometry.

Students are evaluated by a term examination, some midterm examinations, and some quizzes.

#### Textbook and Reference

KindTitleAuthorPublisher
TextbookNo textbook. The original slides and video contents are used.
ReferencesNo reference. The original slides and video contents are used.

#### Requirements(Assignments)

The slides of the lecture should be read. The video contents of the lecture should be viewed.

#### Note

LMS is used in this course.

#### Schedule

1Introduction: Outline of this course. History of geometry.
2Euclidean geometry (1): Parallel postulate (Euclid's fifth postulate).
3Euclidean geometry (2): Pythagorean theorem and its variants.
4Euclidean geometry (3): Triangle centers. Euler line.
5Euclidean geometry (4): Ceva's theorem. Menelaus' theorem.
6Projective geometry (1): Points at infinity. Fundamental theorem of projective geometry. Desargues' theorem.
7Projective geometry (2): Principle of duality. Pascal's theorem. Brianchon's theorem.
8Projective geometry (3): Menelaus' theorem reconsidered. Midterm examination.
9Analytic geometry (1): Basic concepts of analytic geometry.
10Analytic geometry (2): Cartesian coordinate system. Lines and planes.
11Analytic geometry (3): Conic sections. Ellipse. Parabola. Hyperbola.
12Analytic geometry (4): Quadric surfaces. Ellipsoid. Hyperboloid. Elliptic paraboloid.
13Modern geometry (1): Topics on topology.
14Modern geometry (2): Topics on graph theory.
15Modern geometry (3): Topics on computational geometry. Term examination.