Problem Sets

Organized around “important” problems, each exploration includes a historical context, people involved, associated readings, guided problem solving experiences, problem extensions, reflection questions, teacher commentary, writing projects, references, and solution commentaries. Spanning the history of mathematics, the problem sets integrate the areas of algebra, geometry, number theory, probability, and calculus. The intended audience includes students in a mathematics history course, secondary and college mathematics teachers, and anyone interested in exploring mathematical problem-solving in historical contexts. My apologies in advance for any errors you discover, whether they be historical or mathematical

Available Problem Sets

Egyptians' Solution of Algebraic Equations
Egyptians' Use of Unit Fractions
Babylonian Approximation of Square Roots
Babylonian Solutions of the Quadratic
Thales and His Semicircle Theorem
Eratosthenes Measure of the Earth's Circumferance
Squaring of the Lunes
Three Famous Problems of Antiquity
Pythagoras and His Theorem
Euclid's Extensions of the Pythagorean Theorem
Euclid's Exploration of Phi
Pythagorean Triples
Equidecomposition of Basic Geometrical Shapes
The Greek's Geometrical Algebra
Greek Approximation of Square Roots
Chinese Approximation of Square Roots
Using Euclid's Geometry to Solve Quadratics
Archimedes and His Mechanical Method
Archimedes' Estimation of Pi
Archimedes and His Quadrature of a Parabola
al-Khwarizmi's Geometric Solution of Quadratics
Khayyam and His Solutions of the Cubic
Fight Over Solving of the Cubic
Descartes' Geometric Solutions of the Quadratic
Descartes' Transform-Solve-Invert Methold
Fermat and His Quadrature of a Hyperbola
Pascal and His Arithmetical Triangle
Newton's Generalization of the Binomial Theorem
Leibniz and Sums of Infinite Sequences
Leibniz and his Harmonic Triangle
The Problem of Points
Godel and Formal Axiomatic Systems
Page Updated 08.05.2014