Explore the fascinating world of geometric constructibility in this comprehensive 6-hour course. Delve into impossible geometry problems, including angle trisection, cube doubling, and circle squaring. Master compass and straightedge techniques, and gain an introduction to field extensions. Examine the degree of field extensions and understand three impossible constructions. Study Gauss' construction of the regular 17-gon and explore the use of a marked ruler instead of a straightedge. Conclude with an overview of constructibility results, providing a thorough understanding of this intriguing mathematical concept.
Overview
Syllabus
Impossible Geometry Problems: Trisecting Angle, Doubling Cube, Squaring Circle.
Constructibility 1: Compass & Straightedge.
Constructibility 2: Intro to Field Extensions.
Constructibility 3: Degree of Field Extension.
Constructibility 4: Three Impossible Constructions.
Constructibility 5: Gauss' Construction of Regular 17 gon.
Constructibility 6: Marked Ruler instead of Straight edge.
Constructibility 7: Overview of Constructibility Results.
Taught by
math at andrews
