Sesame Street has me flummoxed

January 20, 2015 4:34 AM

Sesame Street, when naming parts of shapes, consistently talks about the number of sides and the number of angles. For example a hexagon has six sides and six angles. This makes me crazy. I thought the pointy parts were "corners" or something like that. Doesn't a shape have infinite angles? If any three points can form an angle? Does 180 degrees not count as an angle? Isn't corner a more precise word?
posted by Owowthathurts to Education (14 answers total)

You define a triangle by the number of sides. But you define what type of triangle by the angles on the insides of the three corners. Just knowing that a triangle has three corners is not useful information - a 2D shape will always have the same number of sides and corners. It's the inside of the corners - the angles - which are important. Understanding that the angles are relevant will be useful to kids later when they learn geometry.
posted by EndsOfInvention at 4:44 AM on January 20, 2015 [12 favorites]

Come to think of it, even just learning what an angle is (in the context of basic geometry - the inside of a corner of a 2D shape) is important.
posted by EndsOfInvention at 4:47 AM on January 20, 2015 [2 favorites]

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points. In other words, a polygon is closed broken line lying in a plane" (Coxeter and Greitzer 1967, p. 51).

Your point about infinite angles is understood. Any N-gon could be a degenerate (N+1)-gon unless, as above, they are defined to avoid that.
posted by vacapinta at 4:51 AM on January 20, 2015 [3 favorites]

Response by poster: That makes senses to me. I was only thinking about how to define the set of shapes, not how to differentiate between types of a set of shapes. It does get the kids accustomed to associating the corner with the interior angle, which becomes very important. It still bugs me because it seems too imprecise, but lord knows as a parent I regularly lay precise on the alter to effective.
posted by Owowthathurts at 4:53 AM on January 20, 2015

It's right in the name of the shape: tri angle. Three angles.
posted by jozxyqk at 4:54 AM on January 20, 2015 [12 favorites]

I've never seen a math textbook talk about "corners," and trust me, mathematicians have plenty of precise terms to use when talking about geometric concepts--only the most basic of which get introduced in a show like Sesame Street. The pointy part is the "vertex" in geometry-speak.
posted by drlith at 4:55 AM on January 20, 2015 [6 favorites]

Response by poster: VERTICES. That's the word mommy brain stole from me! Thank you!
posted by Owowthathurts at 4:55 AM on January 20, 2015 [5 favorites]

I agree with your initial complaint, I don't like saying that a square has "four angles". No, it has four corners (or vertices) which all happen to be the same 90degree angle. If you tell me a triangle has three angles, part of my brain wants to assume you can't possibly be talking about an equilateral triangle.
posted by aimedwander at 5:24 AM on January 20, 2015 [2 favorites]

Well, they should be saying "interior angles"--but it's Sesame Street, so I'll let it slide. I would not be startled if I saw the word angle on a math exam, and would know that it meant the interior angle of whatever shape was presented in the diagram (usually next to a specific letter) unless specified otherwise.
posted by anaelith at 5:30 AM on January 20, 2015 [2 favorites]

Oddly I think of a "corner" as a 90 degree angle. So maybe they are trying to break down that connection?

I think sesame street's primary goal is introduction of reading, writing, social and math skills to young children in preparation for school. In that context I think the use of angels is excellent because it's making children comfortable and familiar with a concept that could otherwise trip them up later. To a large portion of kids sesame street will be the only place they hear these words. So a broad simple explanation is probably best.
posted by French Fry at 6:23 AM on January 20, 2015 [2 favorites]

From Wolfram MathWorld:

"The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle.

In a polygon, the (interior, i.e., measured on the interior side of the vertex) are generally denoted alpha_i or A_i. The sum of interior angles in any n-gon is given by (n-2)pi radians, or 2(n-2)×90 degrees (Zwillinger 1995, p. 270)." [emphasis added]
posted by The Michael The at 6:30 AM on January 20, 2015

Normally you think of (and define) angles as being created where two lines or line segments intersect.

Thus, any polygon has a set of natural angles at the points where each two sides (ie, line segments) intersect.

You can SEE those angles immediately whenever you look at a drawn polygon. Look at the points where the sides (line segments) intersect, and there is an angle drawn for you. There will always be the same number of these angles as sides.

You CAN make a whole bunch more angles in any polygon by taking any three points anywhere on the polygon, then drawing lines through each pair of points, then looking at the angle between those lines. But those angles aren't really natural to the polygon nor are they drawn or visible to observe in normal circumstances.

Just for example, in an octagon, there are eight angles right there, drawn for you, immediately visible to the eye. And that are rather vital to the shape and identification of that particular type of polygon. Then there are an infinite amount of further angles that COULD BE drawn using points on the octagon, that are completely irrelevant to the definition and shape of the octagon.

So Sesame Street is focusing on those angles that are 1) Obvious and already drawn as part of the shape and 2) Important to determining/classifying the shape.

To make some distinctions:

- Sides are the LINE segments

- Vertices are the POINTS where two line segments intersect

- Angles are the ANGLE made between the two intersecting line segments

Those are three different things and three different concepts.

The reason Sesame Street is using the word "angles" rather than "vertices" is because they want the kids to get used to looking at the angle that the two intersecting line segments make, not simply the POINT where they intersect, which is a different thing.

The angle turns out to be very important in our usual way of classifying polygons.

For example, a rectangle and a parallelogram both have four sides and four vertices. The difference between the two is in the angles--right angles vs non-right angles.

A regular octagon has eight equal sides and eight equal angles. Those are the distinguishing factors of regular vs non-regular octagons. A regular octagon must have BOTH of those factors. The fact that it also has eight vertices is irrelevant (all octagons have eight vertices, so that factor doesn't help at all in discriminating between regular and non-regular octagons).

Etc.
posted by flug at 6:47 AM on January 20, 2015 [8 favorites]

And if it makes you feel better: "The word angle comes from the Latin word angulus, meaning 'a corner'."
posted by flug at 6:53 AM on January 20, 2015 [6 favorites]

Not to ruin a good beanplating or anything, but I assume that the angles thing is a pedagogical choice. That is to say, the writers know it's not 100% accurate and precise in context, but the feeling is that it will help introduce young kids to the concept of angles so that later, when it comes time for them to learn geometry in a more formal way, the concept will be less foreign to them.

You wouldn't get that with "corners", and "vertices," while arguably more correct, is a term that many adults are unfamiliar with—so teaching kids to call the corners of a square "vertices" might put them in conflict with their parents. "Vertices" is also a more complicated word, both to say and to write, and it uses an alternative singular/plural system that would be less familiar to young kids.

I can't say for sure that that was the reasoning behind Sesame Street's choice of terminology, of course. Neither do I care to take a position on whether the choice represents sound pedagogy or not. Nevertheless, I assume that something like the above reasoning went into the choice to refer to the vertices of 2D polygons as "angles."

Very often in teaching it makes sense to use a less-accurate term, when doing so helps prepare the ground for the more advanced concepts that will come later in a student's education. This is especially so with young kids who have a limited conceptual and linguistic toolbox to work with, because it rarely makes sense to introduce a concept to a student without anchoring it firmly to an existing concept that they already have mastery over, and with young kids there are just fewer attachment points, so to speak.

Anyway, that's my take on the issue. It's pretty speculative, but I'd stand behind it absent any more definitive research or disclosure on the matter.
posted by Anticipation Of A New Lover's Arrival, The at 8:56 AM on January 20, 2015 [5 favorites]