Mathematical recreations in the Middle Ages (Q2779225)

Addressed to both historians of mathematics and to those who do not find mathematics ``interesting or useful'', this is a comprehensive survey of text problems considered \textit{recreational} showing up in Medieval manuscripts, the most often cited being Alcuin's \textit{Propositiones ad acuendos juvenes}, although problems often originate in older times, being found in the \textit{Greek Anthology} (a collection of number problems in epigrammatic form, assembled by Metrodorus around 500 A.D.) or in the 7th century mathematical collection of the Armenian scholar Anania Širakac'i (for which the author does not cite any reference; \textit{T. Greenwood} [Revue des Études Arméniennes 33, 131--186 (2011)] provides an excellent introduction, translation, and commentary). NEWLINENEWLINEWith 15 chapters and 197 worked-out examples, this is a true treasure trove for Medieval (both Christian and Islamic) recreational mathematics. NEWLINENEWLINEEach chapter is devoted to one theme. Chapter I: Decanting problems (example: In Cologne there were three brothers who had nine jars of wine. The \(n\)th contained \(n\) pails for \(n=1,\ldots, 9\). Divide this wine into equal parts among the three brothers without breaking any jar.); Chapter II: The barrel sharing problem (example: A dying father bestows on his three sons thirty glass vials, of which ten were full of oil, ten other half-full, and the last ten were empty. These should be divided in such a manner that each brother receives the same amount of oil and glass.); Chapter III: The problem of weights (example: A man has a balance with three pieces of weight, adding up to 10 lbs, and they are such that he can weigh any weight from 1 lb to 10 lbs, nothing more and nothing less. Find out how much each piece weighs.); Chapter IV: Distribution problems and divisions (example: A lover entered an orchard to gather apples. Leaving the orchard, he has to give the first guard half of the apples and one apple, the second guard half of the remaining apples and one apple, and the third guard half of the remaining apples and one apple. After which the man has one apple left for his beloved lady. How many apples did he gather?); Chapter V: Faucet problems (example (from the \textit{Greek Anthology}): I am a brazen lion. Two water jets stream out of my two eyes, another one from my mouth, another one from my foot. My right eye fills the pool in two days, my left eye in three, and my foot in four; six hours suffice to fill it through the water jet of my mouth. If all the spouts, of my eyes, mouth, and foot, are open simultaneously for the water to flow, how long will it take for the pool to fill?); Chapter VI: Movement problems (example: Two people leave their two villages, which are situated 105 miles as the crow flies from each other, each walking toward the other village. One of them advances 31\(\frac{1}{2}\) miles a day, the other 21. When will they meet?); Chapter VII: Large numbers, involving geometric progressions, consecutive duplications, the measure of the Earth; Chapter VIII: Combinatorial problems; Chapter IX: Crossing the river (starts with the famous problem how to transport wolf, goat and cabbage safely to the other river bank); Chapter X: Various problems (example: Fibonacci's rabbit problem); Chapter XI: Kinship problems (example: Two men, in no kinship relation to each other have married each other's daughter, and they gave them each a child: what is the kinship relation of the two children?); Chapter XII: Magic squares; Chapter XIII: The movement of the knight over the 64 squares of the chessboard; Chapter XIV: Infinite sets (without bona fide recreational mathematics puzzles); Chapter XV: Chosen numbers guessed and hidden objects. NEWLINENEWLINEFor classical money-changing problems, which are omitted, the author refers to [\textit{J. Tropfke}, Geschichte der Elementarmathematik. Band 1: Arithmetik und Algebra. 4. Aufl. Berlin, New York: Walter de Gruyter (1980; Zbl 0419.01001)].