Based on a historic approach taken by instructors at MIT, this text is geared toward junior and senior undergraduate courses in analytic and projective geometry. Starting with concepts concerning points on a line and lines through a point, it proceeds to the geometry of plane and space, leading up to conics and quadrics developed within the context of metrical, affine, and projective transformations. The algebraic treatment is occasionally exchanged for a synthetic approach, and the connection of the geometrical material with other fields is frequently noted.
Prerequisites for this treatment include three semesters of calculus and analytic geometry. Special exercises at the end of the book introduce students to interesting peripheral problems, and solutions are provided.
About the Author
Dirk J. Struik (1894–2000) was an acclaimed mathematician who taught at MIT from 1926 to 1960. After retirement he continued to lecture at MIT forums and served as an honorary research associate at Harvard's History of Science Department.
Table of Contents
1. Point Sets on a Line
2. Line Pencils
3. Line Coordinates. Homogeneous Coordinates
4. Transformations of the Plane
5. Projective Theory of Conics
6. Affine and Euclidean Theory of Conics
7. Projective Metric
8. Points, Lines, and Planes
9. Projective Theory of Quadrics
10. Affine and Euclidean Theory of Quadrics
11. Transformations of Space
Answers to Exercises