Propositiones ad Acuendos Juvenes/Problems/42 - De Scala Habente Gradus Centum/Historical Note
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Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $42$: De Scala Habente Gradus Centum
David Wells calls to mind the apocryphal story (quite possibly untrue) about Carl Friedrich Gauss, where at the age of $8$ he solved the problem of adding the numbers from $1$ to $100$ in a few seconds.
David Singmaster remarks that the knowledge of how to sum an arithmetic series like this seems to have been known to the ancient Babylonians and ancient Egyptians.
It was also known to the ancient Greeks, but interestingly does not appear in Euclid's The Elements.
Alcuin's is the earliest text which dresses the problem up in fancy clothes, and many European texts follow his example.
In such renditions, the number of elements to add is almost always $100$.
Sources
- 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126) www.jstor.org/stable/3620384
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): 'Propositions to Sharpen Up the Young': $85$