Dicuil (9th century) on triangular and square numbers

Citation

Ross HE & Knott BI (2019) Dicuil (9th century) on triangular and square numbers. British Journal for the History of Mathematics, 34 (2), pp. 79-94. https://doi.org/10.1080/26375451.2019.1598687

Abstract
Dicuil was a ninth-century Irish monk who taught at the Carolingian school of Louis the Pious. He wrote a Computus or astronomical treatise in Latin in about 814–16, which contains a chapter on triangular and square numbers. Dicuil describes two methods for calculating triangular numbers: the simple method of summing the natural numbers, and the more complex method of multiplication, equivalent to the formula n(n + 1)/2. He also states that a square number is equal to twice a triangular number minus the generating number, equivalent to n2 = 2[n(n + 1)/2] – n. The multiplication formula for triangular numbers was first explicitly described in about the third century AD by the Greek authors Diophantus and Iamblichus. It was also known as a solution to other mathematical problems as early as 300 BC. It reappeared in the West in the sixteenth century. Dicuil thus fills a gap in our medieval knowledge.

Journal
British Journal for the History of Mathematics: Volume 34, Issue 2