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· 제목 : Two-Dimensional Spaces, Volumes 1, 2, and 3 (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 기하학 일반
· ISBN : 9781470443238
· 쪽수 : 389쪽
· 출판일 : 2018-01-30
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 기하학 일반
· ISBN : 9781470443238
· 쪽수 : 389쪽
· 출판일 : 2018-01-30
목차
- Volume 1
- Lengths—The Pythagorean theorem
- Consequences of the Pythagorean theorem
- Areas
- Areas by slicing and scaling
- Areas by cut and paste
- Areas by counting
- Unsolvable problems in Euclidean geometry
- Does every set have a size?
- Bibliography
- Volume 2
- The fundamental theorem of algebra
- The Brouwer fixed point theorem
- Tools
- Lebesgue covering dimension
- Fat curves and Peano curves
- The arc, the simple closed curve, and the Cantor set
- Algebraic topology
- Characterization of the 2-sphere
- 2-manifolds
- Arcs in $\mathbb{S}^2$ are tame
- R. L. Moore's decomposition theorem
- The open mapping theorem
- Triangulation of 2-manifolds
- Structure and classification of 2-manifolds
- The torus
- Orientation and Euler characteristic
- The Riemann-Hurwitz theorem
- Bibliography
- Volume 3
- A graphical introduction to hyperbolic geometry
- Hyperbolic geometry
- Gravity as curvature
- Curvature by polyhedral approximation
- Curvature as a length derivative
- Theorema egregium
- Curvature appendix
- Bibliography
