Riemann sum

noun

A certain kind of approximation of an integral by a finite sum that is calculated by dividing the interval of integration into smaller sub-intervals and summing sample values of the integrand inside those sub-intervals multiplied by their lengths.

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Meanings

nounRiemann sum (plural Riemann sums)

plural Riemann sums

  1. mathematicsA certain kind of approximation of an integral by a finite sum that is calculated by dividing the interval of integration into smaller sub-intervals and summing sample values of the integrand inside those sub-intervals multiplied by their lengths.

Origin

Named after Bernhard Riemann, a German mathematician.

Full word history & related roots →

Translations

French somme de Riemann
  • somme de Riemannkind of approximation of an integral
Polish suma Riemanna
  • suma Riemannakind of approximation of an integral
Portuguese soma de Riemann
  • soma de Riemannkind of approximation of an integral
Spanish suma de Riemann
  • suma de Riemannkind of approximation of an integral
Cite this entry
APA

Riemann sum. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Riemann%20sum

MLA

“Riemann sum.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Riemann%20sum. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Riemann sum,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Riemann%20sum.

Source: Riemann sum on Wiktionary, CC BY-SA 4.0.