Trent University
Mathematics 3810H
Ancient and classical mathematics
Archive Page

MATH 3810H, Winter 2022

• MATH 3810H Course Outline
• Supplementary text: A Short Account of the History of Mathematics (4th Edition), by W.W. Rouse Ball, from Project Gutenberg. [Local copy.]
• The Greek Alphabet
• Project
• Assignment # 1, 2, 3, π, 4, 5, 6
  Readings for Assignment # 2:
  Words and Pictures: New Light on Plimpton 322 by Eleanor Robson
  Plimpton 322 is Babylonian exact sexagesimal trigonometry, by Daniel F. Mansfield and N.J. Wildberger
  Reading for Assignment #3:
  Meno, by Plato, translated by Cathal Woods.
  Reading for Assignment #5:
  Archimedes, the Sand Reckoner by Ilan Vardi, including his translation of the Greek text
• Take-Home Final Examination
• Lectures and Notes (webm and pdf formats)
  • (Pre-)History of mathematics - video and notes
  • Ancient Egypt and the Egyptian Number System - video and notes
  • Egyptian Fractions, Division, and Some Algebra - video and notes
  • Ancient Egyptian Geometry - video and notes
  • Ancient Mesopotamia and Their Number System - video and notes
  • Mesopotamian Arithmetic and Algebra - video and notes
  • Mesopotamian Geometry and Algebra - video and notes
  • Beginning of Greek Mathematics - Thales - video
  • Pythagoras - video
  • Zeno of Elea and Hippocrates of Chios - failed to record
  • Eudoxus of Cnidus - video [audio failed]
    Handout: Magnitudes and Proportions
  • Lunes, Three Unsolved Problems, and Archytas of Tarentum - video
  • Mathematics and Philosophy: Plato and Aristotle - video
  • Euclid - video
    Handout: Excerpt from Book I of the Elements
  • Euclid II - video
    Handout: Proposition I-47 - The Pythagorean Theorem
    Handout: Excerpt from Book VII of the Elements
  • Euclid III - video
    Handout: Excerpt from Book VII of the Elements
    Handout: Proposition IX-20 - The Infinitude of Prime Numbers
  • Euclid IV - video
    Handout: Proposition XII-2 - Areas of Circles are Proportional to the Squares of their Diameters
    Handout: Proposition XIII-12 - Area of an Equilateral Triangle Inscribed in a Circle
  • Archimedes - video
    Handout: Archimedes in Plutarch's Life of Marcellus [excerpt]
  • Archimedes II - video
    Handout: The Cattle Problem
    Handout: Quadrature of the Parabola
  • Archimedes III - video
    Handout: The Method (a.k.a. Geometrical Solutions Derived From Mechanics)
  • Ancient Greek and Hellenistic Astronomy - video
  • Claudius Ptolemy - video
  • Apollonius of Perga - video
  • Eratosthenes of Cyrene - video
  • Heron and Menelaus, both of Alexandria - video
  • Diophantus - video
  • Pappus of Alexandria - video
  • The End Times - video

MATH 3810H, Winter 2020

• MATH 3810H Course Outline
• Project
• Assignment # 1, 2, 3, 4, 5, 6
• Take-Home Final Examination
• Supplementary text: A Short Account of the History of Mathematics (4th Edition), by W.W. Rouse Ball, from Project Gutenberg. [Local copy.]
• Instead-of-lecture notes:
  • 2020-03-18 Heron of Alexandria
  • 2020-03-19 Diophantus of Alexandria
  • 2020-03-24 Pappus of Alexandria
  • 2020-03-25 Pappus' Theorem
  • 2020-03-26 Theon and Hypatia of Alexandria
  • 2020-03-31 Proclus and Boethius
• Additional readings:
  • The architect Kha's protractor, by Amelia Carolina Sparavigna.
  • Words and Pictures: New Light on Plimpton 322, by Eleanor Robson.
  • Plimpton 322 is Babylonian exact sexagesimal trigonometry, by D.F. Mansfield and N.J. Wildberger.
  • Meno, by Plato, translated by Cathal Woods.
  • Excerpts from Euclid's Elements:
    • Book I excerpt
    • Proposition I-47, the Pythagorean Theorem
    • Book V excerpt
    • Book VII excerpt
    • Proposition IX-20, the infinitude of prime numbers
    • Proposition XIII-12, relating the the sides of an equilateral triangle inscribed in a circle to the radius
    Taken from Euclid's Elements in Greek, with an English translation by Richard Fitzpatrick.
  • Archimedes' Cattle Problem
  • Geometrical Solutions Derived from Mechanics [also known as The Method], by Archimedes, trans. by J.L. Heiberg and L.G. Robinson. From Project Gutenberg. [Local copy.]
  • The Sand Reckoner [PostScript] by Archimedes, translated with commentary by Ilan Vardi. [Local copy (pdf).]
• The Greek Alphabet

MATH 3810H, Fall 2017

• MATH 3810H Course Outline
• Project
• Assignment # 1, 2, 3, π, 4, 5, 6
• Take-Home Final Examination
• The Greek Alphabet
• Magnitudes and Proportions

MATH 3810H, Winter 2016

• MATH 3810H Course Outline
• Assignment # 1, 2, 3, π, 4, 5, 6
• Take-home Final Examination

MATH 3810H, Fall 2013

• Assignment # 1, 2, 3, 4, 5, 6
• Take-home Final Examination

MATH 3810H, Fall 2011

• Assignment # 1, 2, 3, 4, 5, 6
• Take-home Final Examination

MATH 3810H, Fall 2009

• Assignment # 1, 2, 3, 4, 5, 6
• Take-home Final Examination

MATH 381H, Fall 2007

• Assignment # 1, 2, 3, 4, 5, 6
• Take-home Final Examination

Other sources

This is not an exhaustive list!

Books

• The Heritage of Thales, W.S. Anglin & J. Lambeck
  Springer Verlag, New York, 1995, ISBN 0-387-94544-X.
• A History of Mathematics (2nd edition), by C.B. Boyer and revised by U.C. Merzbach,
  John Wiley & Sons, New York, 1991, ISBN 0-471-54397-7.
• A History of Mathematical Notations, by Florian Cajori,
  Dover Publications, New York, 1993, ISBN 0-486-67766-4.
  (Originally published in two volumes by Open Court Publishing, Chicago, in 1928 and 1929.)
• Classics of Mathematics, edited by Ronald Calinger,
  Prentice-Hall, New Jersey, 1995, ISBN 0-02-318342-X.
• The History of Mathematics, by Roger Cooke,
  John Wiley & Sons, Inc., New York, 1997, ISBN 0-471-18082-3.
• An Introduction to the History of Mathematics (3rd edition), by Howard Eves,
  Holt, Rinehart and Winston, New York, 1969.
• Mathematics in the Time of the Pharaohs, by Richard J.~Gillings,
  Dover Publications, New York, 1982, ISBN 0-486-24315-X.
• Mathematical Thought from Ancient to Modern Times Vol. I, by Morris Kline,
  Oxford University Press, New York, 1972.
• Mathematics in Western Culture, by Morris Kline,
  Oxford University Press, New York, 1953.
• A History of Mathematics, by Jeff Suzuki,
  Prentice-Hall, New Jersey, 2002, ISBN 0-13-019074-8.

Journals

• Historia Mathematica, a journal on the history of mathematics.
  Published by Elsevier. Available at Bata Library, in print and/or electronic form, depending on the issue.

Various general mathematics journals occasionally publish articles about the history of mathematics. Search!

A few online resources

• Ancient language translators (Automated translation from English to Egyptian, Sumerian, and Assyrian/Babylonian).
• The Antikythera Mechanism Research Project.
• Euclid's Elements, with interactive diagrams by D.E. Joyce.
• Euclid's Elements in Greek, with an English translation by Richard Fitzpatrick.
• Google Book Search has the full text of a lot of older works available for reading online and/or for download.
• History of mathematics, main article at Wikipedia.
• History/Biography at The Math Forum
• History of Mathematics at Math Archives (University of Tennessee - Knoxville)
• History of Mathematics at Mathematics Resources on the Internet by Bruno Kevius
• History of mathematics article at Wikipedia
• The History of Mathematics, maintained by David R. Wilkins
• Images of ancient and medieval works on mathematics from Rome Reborn: The Vatican Library & Renaissance Culture, a Library of Congress exhibition.
• Indian Mathematics: Redressing the balance, by Ian G. Pearce.
• MacTutor history of mathematics archives
• A Modern Almagest: An updated version of Ptolemy's model of the solar system, by Richard Fitzpatrick.
• Project Gutenberg has the full text of a lot of older works available for download.
• Web resources on the history of mathematics, maintained by The British Society for the History of Mathematics.
• Wilbour Hall, an archive of "public domain materials that are essential for the study of ancient and early modern mathematics and mathematical astronomy," maintained by Joseph Leichter.

Department of Mathematics

Trent University

Maintained by Stefan Bilaniuk. Last updated 2022-05-04.