Convex polygon

In geometry, a convex polygon is a special type of polygon. It is defined as the boundary of a convex set, which means that if you pick any two points inside or on the edge of the polygon, the straight line connecting them will also stay inside or on the edge of the polygon. This makes the shape very regular and predictable.

A convex polygon is also a simple polygon, meaning it does not self-intersect. Another way to think about it is that if you draw a line that does not touch any of the edges of the polygon, that line will only cross the polygon in at most two places. This property makes convex polygons very useful in many areas of math and computer science.

Because of these special qualities, convex polygons are often used in video games, computer graphics, and many other fields where clear and simple shapes are needed.

Strictly convex polygon

A strictly convex polygon is a special type of convex polygon. In a strictly convex polygon, no straight line can pass through more than two corners of the shape. Also, all the inner angles of a strictly convex polygon are smaller than 180 degrees, unlike in a regular convex polygon where some angles can be exactly 180 degrees.

Main article: interior angles

Properties

A convex polygon is a special kind of shape with straight sides where certain rules are followed. One key rule is that every inside angle is no larger than 180 degrees. Another rule is that if you pick any two points inside or on the edge of the polygon and draw a line between them, that line will stay inside or on the edge of the polygon.

Convex polygons also have other interesting properties. For example, if you combine two convex polygons, the shape you get will still be convex. You can also split a convex polygon into triangles by drawing lines from one corner to the other corners. Additionally, every convex polygon can fit perfectly inside a triangle that is no more than twice its size.

Strict convexity

A polygon is called "strictly convex" when it meets certain special rules. For example, every angle inside the polygon is less than 180 degrees. Also, if you pick any two points inside the polygon or on its edges (but not on the same edge), the line connecting them stays inside the polygon, except at the points themselves.

Triangles are always strictly convex because they are the simplest shapes with three sides.