1

The English language uses a different form for regular polygons of three or four sides than for five and larger.

Is there a math-historical explanation?

David G. Stork
  • 29,774
BMeph
  • 111
  • I use quadrilateral instead of quadrangle :). Dunno about the answer, but I suspect it's similar to 1st, 2nd, 3rd, being different from 4th onwards. – Rushabh Mehta Jul 28 '20 at 01:28
  • ...and we use tetrahedron... – J. W. Tanner Jul 28 '20 at 01:28
  • Trigon shows up in trigonometry, for one example. – DreiCleaner Jul 28 '20 at 01:31
  • 1
    Maybe ask instead at https://english.stackexchange.com/ – Ethan Bolker Jul 28 '20 at 01:38
  • is angle in rectangle a coincidence? – Calvin Khor Jul 28 '20 at 01:42
  • We do use trigonal bipyramid instead of triangular bipyramid. – SarGe Jul 28 '20 at 01:42
  • 1
    Maybe its because we use common english words for common shapes, but greek derivatives for regular polygons since they were studied by ancient greeks? hexagon late 16th century: via late Latin from Greek hexagōnon, neuter (used as a noun) of hexagōnos ‘six-angled’. quadrangle late Middle English: from Old French, or from late Latin quadrangulum ‘square’, neuter of quadrangulus, from Latin quadri- ‘four’ + angulus ‘corner, angle’. triangle late Middle English: from Old French triangle or Latin triangulum, neuter of triangulus ‘three-cornered’ (see tri-, angle1). [from computer dict] – Calvin Khor Jul 28 '20 at 01:46
  • Google's word origin section is useful: latin word for straight (right, imo)+ latin word for angle, interestingly though, "Quadra" in Latin, is "esquare" (or similar) in old French – UmbQbify Jul 28 '20 at 02:31

1 Answers1

1

Quadrilateral is perhaps more common that quadrangle, but both have habitual uses. These two words and triangle all have Latin roots. The shapes are extremely common in other walks of life and, as part of mediaeval Latin, became adopted into common English.

The terms pentagon, hexagon, etc. are of earlier Greek origin. They are not such common shapes and would only have been talked about by those with knowledge of geometry and a respect for Euclid's Elements. They stayed that way. The Greek equivalents of the first two are trigon and tetragon. These nouns are occasionally used by pedants (like me), surviving mainly in the adjectives trigonal and tetragonal.

A further complication arises from the study of configurations, or regularly structured arrangements of points and lines in the plane. A distinction was made between the complete quadrilateral, which has four lines (laterals) meeting in pairs at six different points and three points on a line, and the complete quadrangle, which has four points (angles) with six lines meeting three at a point.

In the case of the triangle there is only one figure, comprising three lines meeting in three points, so no disambiguation is necessary. Moreover such as simple two-on-two cycle is regarded as a mere polygon, too degenerate to be a proper configuration. Worse, whether a "triangle" is assumed to have complete lines or rather a circuit of finite segments became moot. By the star of the 20th century many geometry texts (e.g. L. Lines; Solid geometry) tended to ignored the issue on the grounds that it did not matter, or define a triangle as having the full infinite line but draw it from that moment on as a finite circuit.

Guy Inchbald
  • 944
  • 5
  • 10