THE THEORY OF IRRATIONALITIES OF THE THIRD DEGREE

By ISABELLA MILLER

CONTENTS 1 INTRODUCTION 2 SUBSTITUTIONS, CENTRAL TILES AND BETA-NUMERATION 3 MULTIPLE TILINGS INDUCED BY THE CENTRAL TILE AND ITS SUBTILES 5 GRAPHS THAT CONTAIN TOPOLOGICAL INFORMATION ON THE CENTRAL TILE 6 EXACT STATEMENTS AND PROOFS OF THE MAIN RESULTS 7 TECHNICAL PROOFS AND DEFINITIONS 8 PERSPECTIVES