Editing Figurate number (section)

== Terminology ==

Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number".<ref>{{citation |editor1-last=Simpson |editor1-first=J. A. |editor2-last=Weiner |editor2-first=E. S. C. |title=Figural number |encyclopedia=The Compact Oxford English Dictionary |edition=2nd |location=Oxford, England |publisher=Clarendon Press |date=1992 |page=587}}</ref>

In historical works about [[Greek mathematics]] the preferred term used to be ''figured number''.<ref>{{citation |title=[[A History of Greek Mathematics]] |author-link=Thomas Little Heath |first=Sir Thomas |last=Heath |volume=1 |year=1921 |publisher=Oxford at the Clarendon Press}}</ref><ref>{{citation|title=Greek Mathematical Philosophy |first1=Edward A. |last1=Maziarz |first2=Thomas |last2=Greenwood |year=1968 |publisher=Barnes & Noble Books |isbn=978-1-56619-954-4}}</ref>

In a use going back to [[Jacob Bernoulli]]'s [[Ars Conjectandi]],<ref name="Dickson" /> the term ''figurate number'' is used for [[triangular number]]s made up of successive [[integer]]s, [[tetrahedral number]]s made up of successive triangular numbers, etc. These turn out to be the [[binomial coefficient]]s. In this usage the [[square number]]s (4, 9, 16, 25, ...) would not be considered figurate numbers when viewed as arranged in a square.

A number of other sources use the term ''figurate number'' as synonymous for the [[polygonal number]]s, either just the usual kind or both those and the [[centered polygonal number]]s.<ref>{{citation |url=https://mathigon.org/course/sequences/figurate#full |title=Figurate Numbers |website=Mathigon |access-date=2021-08-15}}</ref>