2-sided shapes

[bemahan]

Hi! My 10 yr old's maths teacher told him that there are no 2-sided shapes and he wants to know if this is right, please? Is a crescent or the centre of a vesica piscis 2-sided? And why isn't a semi-circle a 2-sided shape? Thank you!

[ailie]

There are 2 sides to everything

[Ice.Maiden]

You are right, bemahan.
A semi-circle is is a two-dimensianal geometric shape.

[factor-fiction]

There is an interesting debate to be had about whether a circle has one side or an infinite number of sides. If it has an infinite number then I suggest a semi circle and crescent have an infinite number too. I'm afraid I don't know what a vesica piscis is.
I assume the teacher is talking about straight line shapes.

[TCL-MUMPING]

Can't say I've heard of a vesica piscis but having just looked it up, that was a shape I thought on right away, What about a flat solid in the shape of the letter "D" too?

[Ice.Maiden]

If you fold a circle of paper in hald, it has a a straight side and a curved side. This is why it's classed as a 2-sided shape.

[factor-fiction]

Yes it's a semi circle, as is a D shape. But if it's a piece of paper folded in two then it also has thickness, so that's another side. Anyway, I'm not sure a curved edge counts as a side. The teacher may have been talking about polygons- and a semicircle isn't a polygon.

[TCL-MUMPING]

Wikipedia says, "In geometry a digon is a degenerate polygon with two sides (edges) and two vertices."

[wildwood]

A circle has two sides... an inside and an outside.

I was going to give you an elaborate and comprehensive scientific reason why there are no 2-sides shapes....
but my breakfast is ready and by the time I've finished that I'll no doubt have forgotten what it was ;-)

[Milvus]

there is of course that unique object, a single sided shape - the Moebius strip.
To create one, take a strip of paper, 12 ins x 1 in. Make a single turn, and join the ends together. With a pencil draw a line lengthways down the strip back to the point you started. You now have a line covering the whole strip and its apparent 2 sides yet that line crossed no boundaries, so a single side with a single boundary

[solera]

Don't forget a sphere 2 sides outside inside.

[factor-fiction]

Did you take this up with the teacher, bemahan?

[bemahan]

Hi! We mentioned it on Friday night (at a school quiz night!) She says she's just talking about shapes with straight sides as they are only at that stage (primary school)

[Michael_Cullen]

It took me a long time to think about it but I have come to the conclusion that there is in fact a two-sided shape. A circle is classed as a one sided shape, because it has no corners but if however, you cut a circle in half and draw a line down the cut you actually get a semi-circle, which would have one circular side and one straight with corners, making it a two-sided shape.

[Aldakin]

()
connect them, you get a two as sided shape.

[jim360]

Strictly speaking, a side has to be a straight line (at least, in normal geometry). Hence, a semicircle is not regarded as a two-sided shape, as one of its "sides" would be a curve (ie not a side), and as a result the smallest number of sides a shape can have is three.

I'd also be careful in regarding a curve as an infinite number of sides -- all statements about infinity are fraught with danger unless you go to infinity in "the right way". A curve is a curve; it can only ever be approximated by straight lines, never replicated exactly.

[HMac9]

Arguments take on a 'shape' and have 2 sides. But sometimes each side of an argument can be just like 2 sides of the one coin! That might not be as cray a way of reasoning as it at first seems in an era where we perhaps still think in static terms. But I think it good to encourage kids to keep their thoughts from settling too soon on one view point. I was looking at this book https://books.google.com.au/books?id=sTVZBwAAQBAJ&pg=PA83&lpg=PA83&dq=empathy+and+geometrical+shapes&source=bl&ots=7HXttviNNv&sig=pS7TT4qdJ3LgiTYUuLdHM9vQyzw&hl=en&sa=X&ved=0ahUKEwio4LaIvOHaAhUKwbwKHUqEA-EQ6AEIXDAL#v=onepage&q=empathy%20and%20geometrical%20shapes&f=false (Around page 86) it's talking about how we see shapes of things and how that can be stirred up, as in someone in an Earthquake perceiving (the shape of) bodies flying through the air even as their own self was also being tossed about by the powerful forces. The book is called "Choreographing Empathy." Empathy can be considered to be a part of the shape of society and choreography is really the arranging of moving shapes in (moving or static?) space as seen by a (static or moving?) observer. Don't forget that Nikola Tesla was a brilliant scientist and mathematician ... and he thought about shape differently to the confines of his time.