What is the Difference Between Concave and Convex?

The main difference between concave and convex lies in the curvature of the surfaces they describe. Here are the key distinctions:

• Concave: A concave surface curves inward, like the inside of a bowl or a spoon. The term "concave" can be easily remembered as it contains the word "cave," which also curves inward.
• Convex: A convex surface curves outward, like the outside of a contact lens or a football. The term "convex" can be remembered by associating it with the word "vex," as it can be vexing to distinguish between concave and convex.

Some everyday examples of concave and convex shapes include:

• Concave:
• The inside of a bowl
• A satellite dish
• A skateboard ramp
• Convex:
• The outside of a contact lens
• An eye
• A speed bump
• A magnifying glass
• A globe

In mathematics and science, the terms concave and convex are often used to describe the curvature of objects or functions. For instance, concave and convex lenses are used in various applications, such as eyeglasses, microscopes, and magnifying glasses.

Comparative Table: Concave vs Convex

The main differences between concave and convex shapes can be summarized as follows:

• Curvature: Concave shapes curve inwards, while convex shapes curve outwards.
• Interior Angles: For polygons, all interior angles in a convex shape must measure less than 180 degrees, whereas at least one interior angle in a concave shape must measure more than 180 degrees.
• Diagonals: In a convex polygon, all diagonals must be held within the shape, while at least one diagonal in a concave polygon must be outside of the shape.

Here is a table summarizing these differences:

These differences are also applicable to mirrors and lenses, where concave mirrors and lenses focus incoming light rays to a focal point, while convex mirrors and lenses diverge incoming light rays.