I graduated high school in 1980, and as a second career, am helping HS students with their math. I just finished my 6th year of this, and have just one question about the change noted in the title.

I recall Septagon, Octagon, Nonagon, Decagon, being figures with sides numbering 7,8,9,10. As a child, I noted that these prefixes reflected those of the last 4 months on the calendar. From this a teacher explained that the calendar months got shifted around, and that at one time September thru December were, in, fact, months 7-10.

A few years ago, I ran into a seven sided figure and a student telling me it was a Heptagon. I do understand that Sept is Latin and Hept is Greek, but would like to know when and more important, why, this change was made.

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    $\begingroup$ I rather suspect that there's no rigid requirement to use either name. It's not like these polygon names are part of the ISO nomenclature :-) $\endgroup$ – Carl Witthoft Jul 23 '19 at 13:00
  • $\begingroup$ What I am looking for may not be so clear, i.e. it seems there was no time (like say, when Pluto was cancelled, as a planet) when there was an announcement "we are changing the naming convention of 7 sided figure". And my gap adds to the mystery. I wonder what the experience was for those teaching this whole time. $\endgroup$ – JTP - Apologise to Monica Jul 24 '19 at 16:54

It is only a recent mistake.

See : Anthony Lo Bello, Origins of mathematical words (John Hopkins UP, 2013),

Septagon This vox nullius is a learned mistake for heptagon. People of some education make a certain type of error not committed by the multitude, and this word is an example of one such mistake, viz., the confusion of languages. Knowing that they need a foreign word for seven, they take the familiar Latin word instead of the required but unfamiliar Greek word and concoct the hybrid septagon on the analogy of the common term pentagon. Related absurdities are automobile, homosexual, neuroscience, sociopath, television, etc. Any such word may be immediately identified as modern. The word septagon appears in Herstein’s Topics in Algebra (first edition, 1964) on pages 190 and 341, an example of a mathematical Homer nodding. It was corrected to heptagon on page 242 of Abstract Algebra, Macmillan, New York, 1986.

See Tripod : Heptagon : In 1551 in Pathway to Knowledge Robert Recorde used septangle. Heptagon appears in English in 1570 in Sir Henry Billingsley’s translation of Euclid’s Elements.

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  • $\begingroup$ Septagon also appears in the 1975 2nd edition of Topics in Algebra (FYI, I had a 2-semester undergraduate abstract algebra course using this during the 1976-1977 academic year), on p. 231. Incidentally, the index entries for "Regular septagon" and "Septagon, regular", both on p. 386, incorrectly cite p. 232. I checked several 1960s-1970 high school geometry texts I have and couldn't find either name mentioned. My HS text (actually, the edition/printing used roughly 3 to 7 years prior my time), Geometry by Edwin E. Moise and Floyd L. Downs (1966), has the following (continued) $\endgroup$ – Dave L Renfro Jul 23 '19 at 16:49
  • $\begingroup$ on p. 514, which is similar to what I found in some of the other HS level geometry texts I have: "Thus we might refer to triangles and quadrilaterals as $3$-gons and $4$-gons, although these terms are seldom used. Similarly, $5$-gons are called pentagons, $6$-gons are hexagons, $8$-gons are octagons, and $10$-gons are decagons." I'm pretty sure $7$-gons were left out because they are not ruler-and-compass constructible, and thus there do not exist "high school explicit" expressions for their various mensuration relations. $\endgroup$ – Dave L Renfro Jul 23 '19 at 16:59
  • $\begingroup$ There is erudition and there is pedantry. Or do we really need to say "longivision"? $\endgroup$ – fdb Jul 23 '19 at 17:16
  • $\begingroup$ @fdb I sure hope not, since it looks like "longDivision $\endgroup$ – Carl Witthoft Jul 23 '19 at 19:45
  • $\begingroup$ If a heptagon were a septagon, then surely a hexagon would be a sexagon. I can't see that one allowing a high-school teacher to get through a geometry lesson. $\endgroup$ – Robert Furber Jul 27 '19 at 19:09

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