Dicuil (9th century) on triangular and square numbers. Issue 2 (4th May 2019)

• Record Type: Journal Article
• Authors: Ross, Helen Elizabeth; Knott, Betty Irene
• Is Part Of: British journal for the history of mathematics. Volume 34:Issue 2(2019)
• Page Start: 79
• Page End: 94
• Publication Date: 2019-05-04
• Subjects: Mathematics -- History -- Periodicals; Mathematics; History; Periodicals; Periodicals; 510.9
• DOI: 10.1080/26375451.2019.1598687
• Languages: English
• ISSNs: 2637-5451

Abstract

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.