Method 1: shooting method and problem-solving ideas!

From the concept of line segment, we know that a line segment is composed of straight lines with two endpoints. Then we take the leftmost endpoint as the starting point to count the line segments, and there are four line segments (red lines). There are three line segments (green lines) from the end of the left 2; And so on, left 3 has 2 lines (blue lines), left 4 has 1 line (yellow lines), and a * * *, 4+3+2+ 1 = 10 line segment.

Method 2: solve the problems one by one!

We all know that one of the necessary conditions of a line segment is that it has two endpoints. Since each line segment has two endpoints, the line segment between two adjacent endpoints is 1 basic line segment, so there are four basic line segments in the figure. There are three line segments composed of basic line segments, and so on, there are two line segments composed of three basic line segments; There are 1 line segments, which consist of four basic line segments. So a * * in the figure has 4+3+2+ 1 = 10 line segments.

Method 3: marking methods and problem-solving ideas!

In fact, notation evolved from method one. When this line has five endpoints, there are four from the leftmost point, which are 3, 2, 1, 0 in turn. Then add these numbers to get the total number of line segments; When this line has six endpoints, there are five from the leftmost point, followed by 4, 3, 2, 1, 0. The result of adding these numbers is the total number of line segments.

When we try to count several lines like this again, we will find a rule that the total number of line segments = (the number of end points of a line-1)+ each number decreases 1 +0. This is the origin of notation.