## A Shape With Many Wives…

### January 5, 2013

#### …or talking to teenagers about Geometry

I’ve been having conversations with some high school students about things having to do with math. I thoroughly enjoy these conversations, as I am intrigued by the way students make sense of the sometimes elusive concepts of algebra, geometry and trig. While looking over some problems I asked a young man Andrew if he knew the definition of a polygon. After letting him flail a bit I resorted to Latin. I know that sounds bizarre, but it seems to me that kids have a knack for making and retaining connections if can connect to the root of a word. So I put forth the question ‘do you know what *poly *means” The answer was no. Hmmm…”Well, do you know what* polygamy* is?” It turns out that nearly all teenager do have a general (though not precise) understanding of polygamy as having many wives. Great*…poly*, therefore, means *many. *A polygon, therefore, must be a shape with many wives…well, not exactly, but I suspect that this is a close enough definition to help a teenager remember that a polygon is a shape with more than two angles and more than two sides.

A discussion of Isosceles Triangles delighted me beyond measure. When I asked my young friend Lucy about an isosceles triangle, she defined it to me as the one with the two lines. I knew exactly what she was talking about: each time students see an isosceles triangle in their math books, there are lines on the two equal sides (like on the orange triangle in the drawing above), which is math nomenclature for “hey, look, these two sides are equal.” It turns out that some kids don’t really know that these little lines are code that math people use to show that line segments are equal, or that you can have an isosceles triangle without having those two lines drawn.

It’s a good thing that I didn’t have to resort to Latin to explain isosceles, as the word isosceles comes to us from Greek, and can roughly be translated as “equal legs.’ I mentioned this to my daughter and she declared,

“I’m an Isosccles!” I suppose it might be more correct to say, “I have isosceles”…?

Thankfully, Equilateral Triangles are Latin-friendly, translating into something like “equal sides.” But this makes me pause and consider some other thoughts about math. Think about this: math is supposedly elegant and logical, however, the name for a triangle with three equal sides comes from Latin, the name for a triangle with two equal sides comes from Greek, and to meaure their lengths the we use Arabic numerals (our 1,2,3,4, 5, etc.), which actually originated in India. No wonder math can be such a challenge! Not only does it seem like a foreign language, fact is, it is many foreign languages!

That said, an understanding of bookbinding (much of which has its roots in Chinese and Japanese cultures) is supported by having a good understanding of geometry.

A bit late, but all the same, I wish you peace in the New Year and may you make connections that support and enrich your life.

January 17, 2013 at 6:54 pm

Dear Paula,

I have been on your blog reading about Blizzard Books. I discovered the technique on Pinterest. I would love to make one but much larger. Would you be so kind to email me some dimensions for larger formats…..about the size of a post card or 4×6 photo. I am retired teacher but not a math instructor!

Thank you.

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January 18, 2013 at 3:47 pm

I don’t have these dimensions handy, but give me some time and I will try to work them out. I am assuming that you want to make it so that the pockets will hold 4 x 6 photos? Let me know.

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September 29, 2013 at 12:51 am

The word “isosceles” (greek “ισοσκελές”) is an ajective that exactly means “one who has equal legs”, so it is not correct to say “I have isosceles” but “I am an isosceles (triangle)”.

As regards the word “γωνία” it means “angle” so “polygon” (“πολύγωνο”) is a shape with many angles and “τρίγωνο” is a shape with three angles.

Greetings from Greece..

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September 29, 2013 at 1:13 pm

Thank You!!! I will tell my daughter she had it right the first time when she declared herself to be an isosceles!

BTW…your needlebook http://noulinaki.blogspot.gr/2013/05/harikuyo-needlebook.html is lovely.

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April 9, 2014 at 10:46 pm

[…] them out. First, you will notice that a preliminary step towards hexagonism is that you create an equilateral triangle , which is just the first of the many perks of this activity. The second, most extraordinary flash […]

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