Wikipedia:Reference desk/Archives/Mathematics/2017 April 23

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

April 23

Coiled Phone Cord

I have tried this experiment repeatedly. If I pick up the handset of a landline phone cord, make a call, and then hang up, I invariably find the cord has become tangled by several loops. Even if I let the cord hang free, so that it lies untangled, after the next call, it will have multiple loops in it. At most I might change hands once or twice, but that does not in my mind account for it then having six or more loops in it when I hang up. Any material that addresses this? Thanks. μηδείς (talk) 02:43, 23 April 2017 (UTC)

• [1] gets multiple interesting hits. [2] has some terminology. Our article tangle (mathematics) isn't much help, though. 73.71.213.123 (talk) 08:05, 23 April 2017 (UTC)

Classifying n-gons

I could have asked this question at any time, but it came to my attention when I saw recent edits to the polygons template.

Triangles can be classified as:

1. Equilateral = 3 lines of symmetry, all sides are equal and all angles are 60 degrees.
2. Isosceles = 1 line of symmetry, 2 sides are equal and one side is different; 2 angles are equal and one angle (the angle formed by the legs) is different.
3. Scalene = no lines of symmetry, no congruent sides and no congruent angles.

To generalize these 3 classifications of triangles into n-gons for n > 3, we can do so as follows:

The generalization of the equilateral triangle is clearly the regular polygon. This is the square for n = 4.

But how about generalizing the isosceles triangle?? An isosceles polygon (a generalization of an isosceles triangle) would be a polygon that is not regular but that has at least one line of symmetry. The non-square rectangle, rhombus, kite, and isosceles trapezoid are all examples of isosceles quadrilaterals.

Likewise, a scalene polygon is a polygon with no lines of symmetry. I don't know whether to categorize a polygon with no lines of symmetry but rotational symmetry (a parallelogram that's not a rectangle or a rhombus) is correctly classified as scalene.

These categories can continue for n-gons for any value n. Do isosceles polygons in general have special properties?? How about scalene polygons in general?? Georgia guy (talk) 12:09, 23 April 2017 (UTC)

Properties of scalene polygons in general would be properties of all polygons. These would be in the article Polygon. As for all polygons with a line of symmetry, you could look at Isosceles trapezoid or Rhombus, and see if any of the properties there generalize. Loraof (talk) 18:59, 23 April 2017 (UTC)

The three disjoint sets into which triangles are classified (by some) do not easily extend to other polygons. Classification follows an inclusive structure for other n-gons. I would regard the concept of "scalene polygons" as original research and therefore inappropriate for Wikipedia (but you are welcome to prove me wrong) Dbfirs 11:13, 25 April 2017 (UTC)

One approach would be to look at the symmetry group of each regular polygon, determine the subgroups, and then find geometric examples of the subgroups. For triangles, symmetry group of the regular (equilateral) triangle has 3 rotations (including 360 degrees) and 3 reflections. It basically has 2 subgroups: 1 reflection, which corresponds to the isoceles triangle, and the identity, which corresponds to the scalene triangle. Square symmetry can be divided up in more interesting ways, so you'll get objects (e.g. rectangles) that don't correspond to triangle subgroups, as well as objects that do (isosceles trapezoid). I expect after working out the details up to octagons or decagons, the general properties of any n-gon will become apparent.--Wikimedes (talk) 15:56, 27 April 2017 (UTC)