Explore Euclid's fundamental construction problems from Book I of his Elements in this 42-minute lecture. Delve into the logical structure of mathematics and the importance of constructing mathematical objects before theorizing about them. Learn to construct an equilateral triangle, bisect a line segment, drop a perpendicular line, translate a line segment, and create a triangle given its three sides using only a straight-edge and compass. Gain insights into the practical applications of these problems in modern dynamic geometry software and enhance your appreciation for the historical foundations of mathematical reasoning.
Overview
Syllabus
Introduction
The constructions of Euclid's Book 1
Euclid and the logical structure of mathematics
Proposition 1: Construct an equilateral triangle on a base
Proposition 10: To bisect a line segment
Proposition 12: To drop a perpendicular line to a line from a point not on it
Proposition 2: To translate a line segment
Proposition 2: To construct a triangle given its three sides as segments
Taught by
Insights into Mathematics
