How many parts does n straight lines divide a plane into? 100 articles?

1 straight line divides the plane into up to 2 parts; 2 straight lines divide the plane into up to 4 parts; 3 straight lines divide the plane into up to 7 parts; Now add the 4th straight line It has a maximum of 3 intersections with the previous 3 straight lines, and these 3 intersections divide the 4th straight line into 4 segments, each of which divides the original plane part in two, so the 4 straight lines divide the plane into 7 + 4 = 11 parts at most

Exactly in a similar way, 5 straight lines divide the plane into a maximum of 11+5=16 parts; 6 straight lines divide the plane into a maximum of 16+6=22 parts; 7 straight lines divide the plane into a maximum of 22+7=29 parts; 8 straight lines divide the plane into a maximum of 29 + 8 = 37 parts

In general, n straight lines divide the plane into 2+2+3 at most....n = 1 2 (square of n + n + 2.)

n straight lines divide the plane into two parts at most (n 2+n + 2).

100 straight lines divide the plane into a maximum of (100 2+100+2) 2=5051 parts.

Use recursion or induction (Xueersi 6th Grade Fall Course).

1 straight line divides the plane into up to 2 parts; 2 straight lines divide the plane into up to 4 parts; 3 straight lines divide the plane into up to 7 parts; Now add the 4th straight line It has a maximum of 3 intersections with the previous 3 straight lines, and these 3 intersections divide the 4th straight line into 4 segments, each of which divides the original plane part in two, so the 4 straight lines divide the plane into 7 + 4 = 11 parts at most

Exactly in a similar way, 5 straight lines divide the plane into a maximum of 11+5=16 parts; 6 straight lines divide the plane into a maximum of 16+6=22 parts; 7 straight lines divide the plane into a maximum of 22+7=29 parts; 8 straight lines divide the plane into a maximum of 29 + 8 = 37 parts

In general, n straight lines divide the plane into 2+2+3 at most....n = 1 2 (square of n + n + 2.)

1+(1+n)*n/2

One line can divide a plane into up to 2 parts.

2 Wanghu straight lines can divide the plane into up to 2+2 parts.

3 straight lines can divide the plane into up to 2+2+3 parts.

The 4 staring straight lines are the most kyal, and the plane can be divided into 2+2+3+4 parts.

n straight lines can divide the plane into 2+2+3+4+...n parts, minimum n+1 parts.

n straight lines can divide the plane into n(n+1) 2+1 parts at most.

Therefore, 200 straight lines or cavities can be divided into 200*201 2 +1 = 20101 parts.

This is a problem of finding patterns, and 1 straight line can divide a plane into 2 parts at most.

Two straight lines can divide a segment plane into up to 4 parts.

3 straight lines can divide a flat blind face into up to 7 parts.

4 straight lines can divide a plane into up to 11 parts.

By analogy, 11 sock chain straight lines can be divided into a plane at most (1+1+2+3+4+.).+11) = 67 parts.

Number of straight lines 1 2 3 4 ......n

Divide the plane. The number of blocks 2 4 7 11

1+1 1+1+2 1+1+2+3 1+1+2+3+4 1+1+2+3+4+ …n

The n+1 line and the previous n lines have up to n intersections, and at most n+1 parts.

then s=2+2+3+.n=(n^2+n+2)/2

If there is 1 straight line, then the plane is divided into 2 parts at most;

If there are 2 straight lines, then the plane is divided into a maximum of 4 parts;

If there are 3 straight lines, then the plane is divided into a maximum of 7 parts;

If there are 4 straight lines, then the plane is divided into a maximum of 11 parts;

1=1, 2=1+1, 4=1+1+2, 7=1+1+2+3, 11=1+1+2+3+4,......

The formula for dividing the plane of a straight line is obtained: n straight lines can divide the plane into 1+1+2+3+...... at mostn parts, that is, the plane can be divided into (n(n+1)+2) 2 parts at most, which is reduced to (n 2) 2+n 2+1.

When n is equal to 10, it can be divided into (10 2) 2+10 2+1=56 parts.

0 straight lines, 1+0=1, the plane is up to 1 block;

1 straight line, 1+1=2, the plane is up to 2 pieces;

2 straight lines, 2+2=4, the plane is up to 4 pieces;

3 straight lines, 4+3=7, the plane is up to 7 pieces;

4 straight lines, 7+4=11, the plane is up to 11 pieces;

5 straight lines, 11+5=16, the plane is up to 16 pieces; , n straight lines, 1+n(1+n) 2=(n +n+2) 2, the plane is up to (n +n+2) 2 blocks.

So 10 straight lines, (10 +10+2) 2=56, the plane is up to 56 blocks.

, n straight lines, 1+n(1+n) 2=(n +n+2) 2, the plane is up to (n +n+2) 2 blocks.

So 10 straight lines, (10 +10+2) 2=56, the plane is up to 56 blocks.

Understanding: If there is a straight line to divide a plane, 1 plane is added, so there is a maximum of: 1+(1)=2 (planes);

If there is another line to divide these two planes, 2 planes are added, so there is a total of 1+(1+2)=4 (planes);

By analogy, if there are n straight lines dividing a plane, then there is a total of :

1+1+2+3+4+ …n=1+n (1+n) 2 planes.