Share a written test question [How many parts can a plane be divided into with n straight lines at most]_javascript skills

Copy code The code is as follows:

Question:

The maximum number of parts that can be divided into a plane by n straight lines


Number of lines:

Inner intersection point:

Number of divisions:

Tell me the rules:

①The most divided parts: Number of lines Number of internal intersection points 1

②The number of internal intersection points = the number of internal intersection points (number of lines-1), the newly added line may have intersections with other lines

③ Use recursion to find the number of internal intersection points, and then substitute it into ① to calculate

The above is normal mathematical thinking. Next, I will talk about the practical test knowledge I use, which is the stuff of my code

I have listed some available parameters for 1~5 straight lines:

Line numbers, internal intersection points, diplomatic points, partial numbers

1　 0　 2　 2

2　1　4　4

3　3　6　7

4　6　8　11

5　10　10　16

I found that diplomatic points are meaningless, anyway they are twice the number of straight lines

And the number of parts = the number of straight lines and the number of internal intersection points 1

The number of intersection points within the number of adjacent straight lines forms an arithmetic sequence. The tolerance of this arithmetic sequence is 1, 1-0=1, 3-1=2, 6-3=3, 10-6=4, Looking horizontally, 1 0=1,2 1=3,3 3=6...But this still uses recursion to find the number of corresponding internal intersection points, so looking at the pattern vertically, 2*1=2 3*2= 6 4*3=12...exactly twice the number of internal intersection points