TITLE: Interesting Medieval Mathematics Lecture/Activity Ideas?
QUESTION [11 upvotes]: Recently I have been invited to give a talk about Medieval Mathematics or mathematics in the 500 AD - 1500 AD time frame. I have been researching the time frame for the past week and have found interesting snippets of Arabian mathematicians and Fibonacci. I know it was called the Dark Ages, but I didn't think it would be this dark... The lecture or(inclusive) activity is 45-90 min long and my audience are students at a boarding school I know (well behaved, funny, smart students). 
So here is what I was thinking: Talk about pre-Arabic number systems and arithmetic, talk some about Arabian mathematicians, and then talk about Fibonacci/Golden Ratio and conclusion. For the activity I thought of doing Abacus races or medieval mathematics trivia with prizes (they would appreciate this). What do you guys think? Any ideas/suggestions?

REPLY [3 votes]: You can find a list of mathematicians from this period here and here, with links to biographies.
Alcuin of York wrote Problems to Sharpen the Young around 800 A.D., which is a nice collection of problems of recreational mathematics. Problem 18 is very well known, and I believe this is the oldest reference we have for this problem.
Leonardo Pisano (who acquired the name Fibonacci some 600 years after his death) has some neat number theory in his Book of Squares. He starts with the result $1+3+\dots+(2n-1)=n^2$, and develops from this a number of methods for solving Diophantine equations. The last problem that he solves is to find numbers $a,b,c$ such that the three numbers $a+b+c+a^2$, $a+b+c+a^2+b^2$, and $a+b+c+a^2+b^2+c^2$ all are squares. His solution: $a=35$, $b=144$, $c=360$.
Levi ben Gerson used mathematical induction in France in the early 1300's, giving proofs of formulas such as $C_k^n={n(n-1)\cdots(n-k+1)\over 1\cdot 2\cdots k}$, of $(1+2+\cdots+n)^2=1^3+2^3+\cdots+n^3$, and of the associate law of multiplication for any number of factors. (Reference: Katz.)
The oldest surviving copies of the texts of Euclid and Archimedes were written in the Byzantine empire in the ninth and tenth century. Obviously, there were interest in mathematics in this part of Europe, though what has survived is mostly commentaries on older texts.