Assignment 1: Doing ancient problems in ancient and modern ways

  

Our first assignment of three assignments for this course involves choosing an ancient puzzle and solving it in ancient -- and modern-- ways. The aim is to begin to understand what it might have been like to do these problems with the mathematical/ conceptual tools and approaches of a historical culture, and to understand the equivalences to our contemporary mathematical understandings. This should deepen our understanding of the mathematical ideas involved, and help us appreciate the ingenuity of human cultures over the millennia and around the world.

You should find two partners to work with, and each group will choose a different problem to work on. Each group of three will present:

• their problem and the background to it
• their solutions to it, using both ancient and modern mathematical techniques
• an extension to the problem

...in an interactive 15-20 minute presentation with the class. Presentations will be tentatively scheduled for Oct 5 and 7 . Groups should post their solutions and extensions to your individual blogs by Monday October 5 at 9 AM.

•You are also required to write a short personal reflection after your presentation on what you learned and took away from the process of doing this project.

Here are the problems you can choose from:

• #1-7 From 5000 Years of Geometry (Scriba & Schreiber): Choose from Problems 1.2.1 to 1.2.7 on pp. 25-26. Background information that you need comes from the preceding pages, pp. 15-24. [Note that in problem 1.2.6, there is a typo in formula 1.2.11, which should read "s=1/2(d-(sqrt d^2-c^2)).]

• #8 From Episodes in the Early History of Mathematics (Aaboe):  Problem 1.5, with a preamble that explains a bit about the problem.

• #9 Also from Aaboe: A preamble and a problem on Babylonian calculation of Pythagorean triples.

• #10 Ahmes' loaf sharing problem. Your task, if you choose this one, is to work through the problem as explained in this (translation of) the original papyrus, and to be able to explain how the Ancient Egyptian solution worked, in both ancient and modern terms.

• #11 As Ahmes was going to St. Ives. Your task, if you choose this one, is to work out how these powers of 7 could have been arrived at using Ancient Egyptian calculation methods we have learned, and to be able to show these methods. You should also research how these calculations would have been made in Fibonacci's time (around 1100 AD in Italy), before the introduction of Hindu-Arabic numerals and the algorithms we use today, and to show how these medieval European arithmetic methods worked as well.

Schedule for presentations: Each group will have 15-20 minutes to present, including a brief interactive activity.

Monday Oct 6 

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Wednesday Oct 8

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