Polygon is a fundamental and important concept in geometry, and the relationship between the inner angle and the number of sides of a polygon is a profound mathematical principle in geometry. In this article, we will delve into the law of the sum of angles inside a polygon and reveal the subtle relationship between it and the number of sides.
1.The case of triangles:
First, let's start with the simplest polygon, the triangle. The inner angle of a triangle and always constant 180 degrees is a common sense of geometry. This law gives us an idea of the sum of the inner angles of the polygon.
2.Unique properties of quadrilaterals:
Next, we look at the quadrilateral. The sum of the inner angles of the quadrilateral is variable, but there is still a certain pattern. When the quadrilateral is a convex quadrilateral, its sum of internal angles is 360 degrees. This reveals that each of the inner angles of a quadrilateral has one more right angle compared to a triangle.
3.*Pentagon:
Subsequently, we will look at the pentagon. The sum of the inner angles of a pentagon is 540 degrees, a rule that shows that the sum of the internal angles increases by 180 degrees for each additional side. This linear relationship provides us with a general way to infer the sum of the angles inside a polygon.
4.Extrapolate to any polygon:
From the above **, we can summarize the general situation: the sum of the internal angles of the n-sided is 180° n-2). This is a conclusion based on mathematical induction, and a high-level generalization of the angles and laws within the polygon.
5.Graphic display and practical application:
Through the graphical display, we can clearly see the relationship between the inner angles of the polygon and the number of sides. This law has a wide range of applications in the teaching of mathematics and geometry, and also provides a convenient mathematical tool for solving practical problems.
The relationship between the inner angles and the number of sides of a polygon is a profound and interesting problem in geometry. Through the study of different polygons such as triangles, quadrilaterals, pentagons, etc., we are able to reveal the laws behind them. This kind of law is not only mathematical knowledge, but also the embodiment of mathematical beauty. In the world of mathematics, the mystery of the sum of the inner angles of a polygon allows us to appreciate the depth and charm of mathematics.