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Material Type: Assignment; Professor: Braun; Class: HISTORY OF MATHEMATICS; Subject: Mathematics; University: University of Kentucky; Term: Spring 2008;
Typology: Assignments
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This problem set may be handwritten.
Problem 1: Prove that
3 is irrational.
Problem 2: Extending the comments on page 17 of JTG, during Step 1 of the quadrature of the rectangle, sketch a proof (using compass and straightedge only) that one can bisect a given line segment.^1
Problem 3: Provide an explanation for why squaring a geometric object is called “quadrature.”
(^1) If you are stuck, look at Proposition I.10 of Euclid’s Elements (for an online
version there is a link on the course website. 1