基本説明
Contents: "A Number is a multitude composed of units" (Euclid).-"..there are no irrational numbers at all" (Kronecker).-Rationality, Elliptic Curves and Fermat's Last Theorem.- Algebraic or Transcendential?- Complex Arithmetic... and more.
Full Description
Previous edition of this title was sold 2000 copies in 3 years. This title explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra. Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding. It contains an insert with 4-color illustrations. It also includes numerous examples and worked-out problems.
Contents
"A Number Is a Multitude Composed of Units"—Euclid.- "... There Are No Irrational Numbers at All"—Kronecker.- Rationality, Elliptic Curves, and Fermat's Last Theorem.- Algebraic or Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- Möbius Geometry.- Complex Linear Fractional Transformations.- "Out of Nothing I Have Created a New Universe"—Bolyai.- Fuchsian Groups.- Riemann Surfaces.- General Surfaces.- The Five Platonic Solids.- Finite Möbius Groups.- Detour in Topology: Euler-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.
