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Mathematical Treasures - Antichissimo di Algorismo

Frank J. Swetz and Victor J. Katz

Two illustrations follow from the14th-century Italian codex, Antichissimo di Algorismo. This is one of many algorisms written at this time. They were arithmetics designed to introduce the Hindu-Arabic numerals, their operational algorithms and demonstrate their use in problem solving. The majority of the problems considered in this codex are commercial in nature. A few might be categorized as “recreational problems.” These two are of this nature and have remained favorites over the years. A special feature of this codex is that it contains 42 illustrations, many of which supplement problems. These two illustrations are of this kind.

Another problem from Algorism

The picture found on folio 59 depicts a situation where two men must divide an item equally. The two companions have eight ounces of balm in an eight ounce vase. At their disposal they have two other vases, one holding three ounces, and the other five ounces. How can they accomplish the equal division?


Problem from Algorism

The illustration on folio 60 presents the situation where three couples wish to cross a stream. The small boat they have will only accommodate two persons at a time. How can they all get to the other shore if no man is to cross with another’s wife? This is a variation of the puzzle-type “River Crossing Problem” that has been posed over the centuries in many guises.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Antichissimo di Algorismo," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University