GLIMPSES OF ALGEBRA AND GEOMETRY

By L. DIARE

1 SECTION “A NUMBER IS A MULTITUDE COMPOSED OF UNITS”—EUCLID 2 SECTION THERE ARE NO IRRATIONAL NUMBERS AT ALL”—KRONECKER 3 SECTION RATIONALITY, ELLIPTIC CURVES, AND FERMAT’S LAST THEOREM 4 SECTION ALGEBRAIC OR TRANSCENDENTAL? 5 SECTION COMPLEX ARITHMETIC 6 SECTION QUADRATIC, CUBIC, AND QUARTIC EQUATIONS 7 SECTION STEREOGRAPHIC PROJECTION 8 SECTION PROOF OF THE FUNDAMENTAL THEOREM OF ALGEBRA 9 SECTION SYMMETRIES OF REGULAR POLYGONS 10 SECTION DISCRETE SUBGROUPS OF ISO (R2) CONTENTS 11 SECTION M¨OBIUS GEOMETRY 12 SECTION COMPLEX LINEAR FRACTIONAL TRANSFORMATIONS 13 SECTION “OUT OF NOTHING I HAVE CREATED A NEW UNIVERSE”—BOLYAI 14 SECTION FUCHSIAN GROUPS 15 SECTION RIEMANN SURFACES 16 SECTION GENERAL SURFACES 17 SECTION THE FIVE PLATONIC SOLIDS 18 SECTION FINITE M¨OBIUS GROUPS 19 SECTION DETOUR IN TOPOLOGY: EULER–POINCAR´E CHARACTERISTIC 20 SECTION THEORY: EULER, HAMILTON, AND THE FOUR COLOR THEOREM 21 SECTION DIMENSION LEAP 22 SECTION QUATERNIONS 23 SECTION BACK TO R3! 24 SECTION INVARIANTS 25 SECTION THE ICOSAHEDRON AND THE UNSOLVABLE QUINTIC 26 SECTION THE FOURTH DIMENSION