This problem is actually counting how many line segments the bottom edge contains. It has a formula, the number of line segments =1+2+3+4+...+(n-1), where n is the number of line segments at the bottom, including the head point and the tail point. Then the number of triangles in the figure below is 15. It can be understood in another way, that is, from all the points at the bottom, choose two points at will and ask how many methods have been selected. This is a combinatorial question, and the answer is c (6,2) = 6x5/2 =15.

Here are some other methods and techniques to calculate the number of triangles:

1. violent enumeration method: this is the simplest and most direct method, that is, counting by enumerating the vertices of each triangle and then judging whether a triangle can be formed. This method is suitable for small-scale triangle counting, but not practical for large-scale triangle counting.

2. Combined counting method: This is a relatively efficient method. By using the knowledge of combinatorial mathematics, the counting problem of triangles is transformed into the problem of selecting a certain number of points and then selecting three points from them to form triangles. Specifically, suppose there are n vertices, and the number of triangles formed by three vertices is C(n, 3). It should be noted, however, that this method is only applicable to the case of fewer vertices, because once the number of vertices increases, the number of combinations will be very large and the calculation difficulty will increase.

3. Counting by type: This is a common method, which divides triangles into different types for classification and counting, and then adds up the numbers of triangles of different types. Common classifications are isosceles triangle, right triangle and equilateral triangle. This method requires a deep understanding of the nature and composition of triangles, and at the same time, attention should be paid to the accuracy and completeness of classification.

4. Using graphic transformation: This is a clever way to transform the original graphic into another form that is easier to count, and then count it. For example, divide a square into several small triangles, small squares and small diamonds, then calculate the number of various small figures, and finally add them to get the number of triangles. This method needs to flexibly use the idea of graphic transformation to find a suitable transformation method.