# Concave vs Convex – When to Choose Which One and Why?

Concave vs convex are both words that are commonly used as adjectives. These words describe the surface or outline of a shape. However, these terms are not often used in a regular conversation. To understand the differences between concave and convex, we must first discover how each term is employed in mathematics, mirrors, lenses, and, lastly, creative writing. Let 501words tell you its differences.

The importance of concave and convex exist in science and mathematics. And you will come across these words when talking about mirrors and lenses such as eyeglasses or contact lenses.

## Concave vs Convex

Concave is an adjective for an inward curve of a shape. One good example of a concave shape is the side view mirror of a car, which reflects an inner curve. While convex is the opposite of concave, it is an adjective for a shape that shows an outward curve. The ball used to play American football has the outer curve that we can best use as an example.

### When to use Concave

The processes related to mirrors, lenses, and reflection can describe through the word concave. Due to how the light reflects a mirror, a concave mirror will make a person look taller. Things such as telescopes, cameras, binoculars, and lenses in eyeglasses use concave lenses.

You can still use the word concave, even if not about science or math. For instance, you see an inward curve like the tummy of a thin person or a pothole. You may describe it as concave.

There are some cases in which concave is used as a descriptive but non-literal sense term. The thing might be exaggeratedly described using the word concave like a synonym of a sunken or thin appearance. Concave is also used as a noun in geometry and mathematics like the type of shape or inward curved line.

### When to use Convex

Convex is a noun or a term for a type of shape or an outward curved line that we usually discuss in geometry and mathematics. Here are the examples of concave vs convex used in a sentence:

• This table is unique because it is sloped outwards and convex.
• The snowballs are in a convex form that seemed to be made using an ice cream scoop.
• He is so thin that his cheeks are concave.
• My contact lenses are in a concave shape to fit the eyeballs.

### How To Avoid The Concave Vs Convex Error

Knowing how to avoid the concave v. convex error can save you a lot of time and trouble. These two words have opposite meanings and mixing them up in writing can lead to a lot of confusion. Both terms are commonly used in science and math classes, but are different enough to cause a mishap when used interchangeably. Convex and concave are adjectives and nouns that refer to shapes. They describe the same shape, but the concave one has a cave in its middle.

In math, the difference between a concave and convex function is simply a matter of definition. Convex functions are functions that satisfy the definition of convexity. The Hessian of a function with several variables is positively defined on its domain. This property is a good sign for a convex function. A convex function is a function that meets the definition of the convex type.

A convex function is a function that has the same graph for x and y. A concave function must lie on a graph of a convex problem to be a convex one. If a convex function has a concave problem, a chord from x to y must lie on or below the graph of f.

Sign analysis is a simple procedure that flags unknown expressions. Performing a sign analysis will always result in the right conclusion. It is also possible to perform an affine analysis, which uses a general composition theorem to identify convex and concave expressions. For example, an affine expression of the function f must be convex, if its sign is positive.

## How to Remember the Difference

You can easily remember the difference between concave vs convex. One good tip is to focus on their last syllable. “Cave” for concave and “vex” for convex. The word with an end of “cave” means curving inward. And the one that ends with “vex” which is convex of the opposite that means bent outward.

There are lots of words/phrases that we need to think thrice before we use in writing such as who vs whom, further vs farther, ensure vs insure, and to vs too.

Knowing the differences between these confusing words, you will not just learn how to become a writer or how to write faster. Rather, it is a good start to write content like a pro. So do not just use apps like Grammarly but also, read and study these common confusing terms.

### FAQs

What is concave vs convex?

Concave is an adjective for an inward curve of a shape. One good example of a concave shape is the side view mirror of a car, which reflects an inward curve. While convex is the opposite of concave, it is an adjective for a shape that shows an outward curve.

How to remember convex vs concave?

You can easily remember the difference between concave vs convex. One good tip is to focus on their last syllable. “Cave” for concave and “vex” for convex. The word with an end of “cave” means curving inward. And the one that ends with “vex” which is convex of the opposite that means bent outward.

#### Conclusion

Concave vs convex are words that have something to do with lines and shapes—often used in science, mathematics, or about mirrors or eyeglasses. For example in mathematics, there is convex shapes, convex polygon, concave polygon, basic polygons and things like that.

Concave lenses are used in eyeglasses for people who are nearsighted i.e people who don’t see far-away images clearly and Convex lenses are used in glasses for people who are farsighted. Even in geometry, both the words can be used to describe the shape of polygons and it depends on whether they have any inward-facing angles.

Did we make all things clear on how these terms differ? What else do you want us to dig deeper into meaning? If you have details about concave surfaces, concave surface features, converging lenses, convex things curve, concave things curve or about convex mirrors and concave mirrors, leave your comment down below. Get grammar checking and grammar sources articles from our site.