Allow me to take "Pique Theorem of Polygon Area" as an example-
For example, let's talk about Pique's theorem of finding the area of a polygon with lattice points. According to logic, we need to use the control variable method in four steps-
1. When there are no inner points but only edge points, the relationship between the number of edge points and the number of containing squares: n edges? 2- 1= number of squares;
2. When the number of edges is fixed and the inner point 0, 1, 2, 3 changes, the relationship between the inner point and the number of squares contained: n = the number of new squares;
Third, the Pique formula can be obtained by summarizing one or two of them:
Number of squares in a polygon =N? N side? 2- 1
Fourth, the area of a polygon with grid points = the area of a single grid.
At this point, the teaching of Pique's theorem for finding the polygon area of lattice points is over.
Is this the strict logic of primary school mathematics?
Do you think they can understand? !
Speaking of which, they remember the last formula at most.
As for why? They don't care!
They just think—
It's hard to remember that a formula can kill some lattice polygons, and finally it can be used to show off!
At this time, you ask him again, why is your algorithm right? He will definitely give you a dirty look. Why should I know?
Maybe after a long time, even they forgot this formula, let alone introduce it from the beginning.
Next, let's wait and see a story about the Jedi massacre!
In the classroom, a group of students are listening to the teacher. Because there are too many students, only some students have desks to sit and listen to the class, while the rest can only stand by and listen to the class.
The teacher will charge tuition after class. Students who have desks in the classroom charge one yuan each, and students who attend classes on the side wall of the classroom charge 0.5 yuan at half price. At last, the teacher suddenly remembered that he shouldn't charge tuition by himself, so he had to pay one yuan.
So the total tuition in the classroom, which is the square, is-
Within n? N side? 2- 1
After listening to this story, I can assure you that no one can't remember this formula! So the problem of long-term memory is solved!
Besides, if you ask the student why, I'm sure he can tell you the story!
Does this story have logic?
Don't!
Finally, the teacher himself reduced 1, which can't stand scrutiny!
It works anyway!