Picture a circle. Put a point inside it. Draw two lines from the point at an acute angle out to the circle’s perimeter.
You have a shape that’s similar to a triangle but with two straight lines and one curved line. Basically the same shape as a slice of pizza.
Is there a name for this polygon?
A triangle with a curved side is commonly referred to as a Reuleaux triangle.
The IPA pronunciation is [ʁœlo]. Approximately, hrur-lo.
If I’m understanding the concept correctly, a Reuleaux triangle has three curved sides. I’m thinking about a polygon with two straight sides and one curved side.
If the point is at the center of the circle, it’s a sector. I’m not sure if there’s a more general term for any triangle with an arc for one side.
Yes. Sector of a circle.
Just to nitpick, this shape wouldn’t be a polygon, because all of a polygon’s edges are straight line segments.
But yeah, what @Lumpy said: If the point is at the center, it’s a sector, otherwise I don’t think there’s a name.
A sector.
Though if there weren’t already a name, pizzagon would be appropriate…?
Okay, what’s the name for a region of a plane that’s bound by enclosed curves?
I know a disk is the technical term for a region that’s bound by a circle. But what’s the more general term?
A sector would be one example of the shape I’m describing. But it would also be possible to have similar shapes that aren’t sectors because the point where the two straight lines meet wouldn’t be the center of the curve described by the curved line.
If there are no straight edges, then it’s a “curvilinear shape”.
With a mixture of straight and curved edges, I don’t think there’s any term more specific than “shape”.
But hey, you can take that as an opportunity. If nobody else has come up with a term for something, you can do so yourself.
Lamina might be close to an umbrella term for a planar closed curve.
Wouldn’t “wedge” work wonderfully?
The issue arose because of an online puzzle I saw.
The comments got into arguments where some people were saying the correct answer was three (which is right) but a number of other people were answering with higher numbers because they felt you can have a triangle with a curved side.
So I was wondering if there was a technical term for this shape so we could say something like “Those aren’t triangles. They’re pizzagons. Pizzagons aren’t triangles.”
You would think we would have made advances in the field in the 2300 years since Euclid.
Not a very technical term but I’d call it a pie slice - a regular pie slice being a sector.
We have, plenty of them. But coming up with new names for things isn’t much of an advance.
Still, you’d think “an area of a plane that’s separated from the rest of the plane by an enclosed line” would be a very basic term in geometry.
Calling it a shape seems so imprecise.
Ordered pizza for three hungry teenagers. It arrived an hour ago. Pizzagon.
Pi slice?