Article ID: CBB215002916

Dicuil (9th Century) on Triangular and Square Numbers (2019)


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.

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Authors & Contributors
Stevens, Wesley M.
Bergmann, Werner
Berggren, John Lennart
Burnett, Charles
Zhao, Jiwei
Lampe, Kurt
Sciamvs: Sources and Commentaries in Exact Sciences
Physis: Rivista Internazionale di Storia della Scienza
VIET: Voprosy Istorii Estestvoznaniia i Tekhniki
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften
Arabic Sciences and Philosophy
University of St. Thomas
Edizioni Cadmo
Arab/Islamic world, civilization and culture
Kirik, Novgorodets
Ceulen, Ludolf van
Thomas Aquinas, Saint
Ibn al-Haytham, Abū ʿAlī al-Ḥasan
Time Periods
12th century
14th century
15th century
Early modern
Castille (Spain)

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