Convex and Concave in Geometry

In geometry, an important distinction is made between shapes that are convex and those that are concave. A convex shape is one in which all interior angles are less than 180 degrees. A concave shape, on the other hand, is one in which at least one interior angle is greater than 180 degrees. Let's take a closer look at the difference between these two types of shapes.

Convex Shapes

As we mentioned before, a convex shape is defined as any shape in which all interior angles are less than 180 degrees. Examples of convex shapes include triangles, circles, and squares. One way to think of a convex shape is as a shape that has no "indentations" or "points." All the points on the surface of a convex shape point outward, away from the center of the shape. 

Concave Shapes

A concave shape, on the other hand, is any shape in which at least one interior angle is greater than 180 degrees. An easy way to remember this is that the prefix "con-" means "opposite of," so a concave shape is basically the opposite of a convex shape. An example of a concave shape is a triangle with one point that sticks out (imagine a triangle with its point sticking up like a pyramid). Other examples of concave shapes include crescents and stars. Just like with convex shapes, you can think of concave shapes as having "indentations" or "points" sticking inward, towards the center of the shape. 

Conclusion

To sum things up, convex shapes are defined by their lack of indentations or points, while concave shapes have at least one point or indentation. Additionally, all the points on the surface of a convexshape point outward away from the center, while on a concave shape they point inward towards the center. Now that you know the difference between these two types of shapes, you're well on your way to becoming a geometry expert!

FAQ

What does convex mean in geometry?

A convex shape is any shape in which all interior angles are less than 180 degrees.

What is a convex simple definition?

A convex shape is one in which all interior angles are less than 180 degrees. A concave shape, on the other hand, is one in which at least one interior angle is greater than 180 degrees.

What is a convex example?

Examples of convex shapes include triangles, circles, and squares. One way to think of a convex shape is as a shape that has no "indentations" or "points." All the points on the surface of a convex shape point outward, away from the center of the shape.

What is the convex?

The convex is the set of points that can be reached by a given point P by moving a distance r>0 in a straight line. In other words, it is the locus of points that are at most r units away from P. Formally, the convex hull of a set X is the intersection of all convex sets that contain X.