What are shapes with curved sides called?

Beyond Straight Lines: Let’s Talk About Shapes with Curves!

We all learn about squares and triangles early on, right? Those shapes with their perfectly straight lines. But geometry is so much more than just that! What about those shapes that aren’t all straight edges? What do we even call them? Well, it’s not always a simple answer, actually. There isn’t one single, official term, but a whole bunch of ways to describe them, depending on what you’re talking about.

The easiest way to put it? “Curved shapes.” Makes sense, right? It’s just a general term for any shape that has a curve in it, whether it’s a flat, 2D shape or a solid, 3D one.

Think about it:

• 2D curved shapes: Circles, of course! Also ellipses, those stretched-out circles. And what about arcs, those little bits of a circle’s edge? Even cool-sounding shapes like cardioids fit in this category.
• 3D curved shapes: Picture a sphere, like a ball. Or a cylinder, like a can. Cones, too!

Now, what exactly is a curve? Well, in math terms, it’s any line that isn’t straight and bends smoothly. Fun fact: even a straight line can technically be a curve – a curve with zero bend!

Curves can also be open or closed. An open curve is like a winding road that doesn’t loop back on itself. A closed curve, on the other hand, is like a racetrack, forming a complete loop. Circles and ellipses? Totally closed curves.

Then you have simple and non-simple curves. A simple curve is one that changes direction but never crosses over itself. Think of drawing a figure eight – that’s a non-simple curve because it intersects itself right in the middle!

Okay, so “curved shape” is a good basic term. But sometimes, you need to get more specific. That’s where things get interesting!

• Conic Sections: Remember slicing a cone in math class? Turns out, you can create some really cool curves that way! Circles, ellipses, parabolas, and hyperbolas are all conic sections. The ancient Greeks, like Euclid and Archimedes, were all over these shapes!
• Circular Arcs: We mentioned these earlier, but they’re just pieces of a circle’s edge.
• Curvilinear Figures: This is a fancy way of saying shapes made of curved lines. You can even have a “curvilinear triangle,” which is a triangle where the sides are curved instead of straight! Imagine that geometry class!
• Algebraic Curves: These are curves you can define with equations. Math magic!

Now, here’s a question: Is a shape with curved sides a polygon? Nope! Polygons have to be made of straight lines. So, if there’s a curve, it’s out of the polygon club.

And speaking of curves, you can even measure how much they bend! It’s called curvature. A straight line has zero curvature (because it doesn’t bend at all), and a circle has constant curvature. The smaller the circle, the tighter the bend, and the higher the curvature.

So, there you have it! Talking about shapes with curved sides isn’t always straightforward, but hopefully, this clears things up. “Curved shape” is a great starting point, but knowing the other terms helps you describe things more precisely. Geometry can be pretty cool, once you get the hang of the lingo!