If any rectangle in the graph has (n- 1) points (excluding the two endpoints of this side), then the other side has (m- 1) points (excluding the two endpoints of this side).
These points are parallel lines on the opposite side and intersect with the other side. These two sets of parallel lines divide the rectangle into many rectangles, and the total number of rectangles is (1+2+3+4+) ...+m) × (1+2+3+4+...+n).
"Smart numbers" is a simple permutation and combination problem. It is not only the basis of learning statistical probability, but also widely used in life. By studying this article, students can learn to calculate numbers from simple to complex, without repetition or omission.
Guide students to learn to draw pictures, cultivate the habit of orderly thinking, and feel the mathematical laws contained in problems. "Smart graphics" can use graphics to describe and analyze problems, make mathematical problems concise and vivid, and develop students' geometric observation ability.
1. To correctly count the number of figures, orderly statistics are needed, and the key is to start with basic figures. First of all, it is necessary to find out which and how many basic graphics are included in the diagram, and then count the new graphics composed of basic graphics and find their sum.
2. Line segment counting method: scalar counting method is adopted. Mark the natural numbers 1, 2, 3 ... and add them between every two adjacent points in turn, and then add all the marked natural numbers. This is the number of all line segments, and there are 1+2+3+4+...+(n- 1) line segments.
3. Method of calculating angle: Scalar counting method is used. Mark the natural number 1, 2, 3 ... between every two adjacent rays, plus all the marked natural numbers, that is, the number of all angles, there are 1+2+3+4+...+(n- 1) angles.