Convex polygon

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

A convex polygon is also a simple polygon. It does not self-intersect. If you draw a line that does not touch any edges of the polygon, that line will cross the polygon in at most two places. This makes convex polygons useful in many areas of math and computer science.

Convex polygons are often used in video games, computer graphics, and 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. Also, all the inner angles are smaller than 180 degrees.

Main article: interior angles

Properties

A convex polygon is a special shape with straight sides that follow some rules. One rule is that every inside angle is smaller than or equal to 180 degrees. Another rule is that if you choose 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 have some interesting features. For example, if you join two convex polygons together, the new shape will still be convex. You can also divide a convex polygon into triangles by drawing lines from one corner to the other corners. Also, every convex polygon can fit inside a triangle that is no more than twice its size.

Strict convexity

A polygon is called "strictly convex" when it follows some 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.

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