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.

concave vs convex

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.

On this page, you’ll learn about the following:

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

Unless you have a linear function, it is hard to distinguish whether a convex optimization problem is convex or not. It is more common to think of a convex optimization problem as a linear problem, but convex optimization problems have a much more broad range of problems. There are thousands of possible constraints, and you can have problems with hundreds of thousands of variables. Fortunately, convex optimization problems are easier to solve than linear ones, and you can often solve them reliably and quickly.

Concave functions have positive second derivatives. This means that their graph from -pi to 0 is the same for all x and y. In addition, convex functions have a convex domain. This means that the problem objects have the objective of maximization.

When you have an affine function, you can check whether it is convex or not with the function’s is_quasilinear function. It will return True if the function is convex. If one of the arguments is negative, the scalar product will be quasiconcave.

Another rule is that a function is convex if a single point on the graph of the function is below the curve. If two points are below the curve, the function is not convex. You can determine this by taking a point on a bend and comparing it with the function’s graph.

The graph of a function can be a convex function if the curve is on a convex polygon. You can also determine this by dividing a function’s graph by a line segment between two points. The line segment is below the curve if the points are on the same side of the curve.

Likewise, if a function has two local minima, it is not convex. The gradient of the function’s graph at the local minimum is zero. This means that the gradient of the function’s graph is the minimum in the neighborhood. A non-convex function will stop at this local minimum. You can also use momentum to solve this problem.

The distance ratio function is another example of a convex function. This function is implicitly enforced when you are convex. If the distance from a centrum to a hyperplane is greater than the centrum’s radius plus two maximum roundoff errors, the facet is convex.

In addition, there are some important assumptions to be made. For example, if the function is a quadratic function, you can prove that the function is convex by generating an expression for each m. You can also use a composition rule. This rule states that the product of a non-negative concave function with a positive convex function is quasiconcave.

The CVXR package is a good way to check whether a function is convex or not. This package assumes that you are familiar with R, but you may need to learn some statistics to be successful. It also defines equality and inequality constraints. This package is meant to introduce you to the world of convex optimization.

Lastly, there is the DCP rule. This rule is an important rule to know because it certify the curvature of functions. If the function is convex, then the matrix of all the second partial derivatives is neither positive semidefinite nor negative semidefinite.

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.

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