What does concave on convex mean?
Concave means “hollowed out or rounded inward” and is easily remembered because these surfaces “cave” in. The opposite is convex meaning “curved or rounded outward.” Both words have been around for centuries but are often mixed up. Advice in mirror may be closer than it appears.
How do you know if a surface is concave or convex?
Summary
- Concave surfaces curve inward.
- Convex surfaces curve outward.
What does convex side mean?
more Curved outwards. Example: A polygon (which has straight sides) is convex when there are NO “dents” or indentations in it (no internal angle is greater than 180°)
What is the concave side?
Concave describes an inward curve; its opposite, convex, describes a curve that bulges outward. They are used to describe gentle, subtle curves, like the kinds found in mirrors or lenses. If you want to describe a bowl, you might say there is a large blue spot on the center of the concave side.
Is a triangle convex or concave?
A polygon is convex if all the interior angles are less than 180 degrees. If one or more of the interior angles is more than 180 degrees the polygon is non-convex (or concave). All triangles are convex It is not possible to draw a non-convex triangle.
Is a triangle concave?
A triangle can never be concave, but there exist concave polygons with n sides for any n > 3. At least one interior angle does not contain all other vertices in its edges and interior. The convex hull of the concave polygon’s vertices, and that of its edges, contains points that are exterior to the polygon.
What means convex shape?
A convex shape is the opposite of a concave shape. It curves outward, and its middle is thicker than its edges. Just like concave, convex can be used as a noun for a surface or line that curves outward, and it also has a use in geometry, where it describes a polygon with interior angles less than or equal to 180°.
What shape is concave?
Convex. Concave describes shapes that curve inward, like an hourglass. Convex describes shapes that curve outward, like a football (or a rugby ball).
Are triangles concave?
A triangle can never be concave, but there exist concave polygons with n sides for any n > 3. An example of a concave quadrilateral is the dart. At least one interior angle does not contain all other vertices in its edges and interior.
How to tell when a function is concave or convex?
We can use the second derivative of a function f (x) to tell when it is concave or convex as follows: If the second derivative of the function is negative, then the function is concave (also called concave down). In symbols, this would mean f’’ (x) < 0.
When does concave up and concave down mean the same?
But then concave up should equal convex down, i.e., the curve is the top (up) part of a concave region. Concave down then equals convex up, meaning that the curve is lower part of a concave epigraph or the upper part of a convex hypograph.
Where does the word concave come from in optics?
As far as I know the etymology went as follows: Like “convex”, the word “concave” has a prior use in optics. Concave (inward-curved) lenses are the opposite of convex lenses, so there is a pre-existing word for “not convex” or “convex in the opposite direction”.
What does a concave up graph look like?
Concave up (also called convex) or concave down are descriptions for a graph, or part of a graph: 1 A concave up graph looks roughly like the letter U 2 A concave down graph is shaped like an upside down U. More