Dicuil (9th century) on triangular and square numbers. Issue 2 (4th May 2019) - Ross, Helen Elizabeth; Knott, Betty Irene
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 n 2 = 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.