Sage-Tips

What is the maximum number of intersections for 10 lines in the same coordinate plane?

There are a maximum number of 45 intersections if ten lines are drawn.

What is the maximums number of regions into which plane can be divided by n straight lines?

One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions, and so on. When the nth line is added to a cluster of (n-1) lines then the maximum number of extra regions formed is equal to n.

What is the maximum number of such regions as a function of n the number of straight lines?

The maximum number Ln of regions in the plane that can be defined by n straight lines in the plane is: Ln=n(n+1)2+1. This sequence is A000124 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

What is the maximum number of regions that can be formed if you draw six lines across the circle?

31
The maximum number of regions that we can obtain from crossing chords with 6 points is 31. Students quickly realize that if 3 or more chords cross at the same point in the interior of a circle, then they don’t obtain the maximum possible number of regions.

How many intersections can 10 lines have?

45 points
If follows, then, that the maximum number of points of intersection when 10 lines are drawn in a plane would be the 8th term in the sequence, or 45 points.

What is the maximum number of points in which two distinct straight lines intersect?

one point
Hence two distinct lines can intersect at most at one point as shown in figure.

What are regions in a plane?

Portion of a plane bounded by a closed simple curve called the boundary of the region. A closed curve divides the plane into two regions: an interior region formed by the points located inside the closed curve and an exterior region formed by the points located outside the closed curve.

What is the maximum number of regions formed by 5 zigs?

5*5=25.

How many times can 5 straight lines intersect?

Five lines can intersect in at most (52−5)/2=10 ways.

What is the maximum number of points of intersection of three lines in a plane What is the minimum number?

Minimum number of point of intersection of three lines on a plene is zero when all the three lines are parallel to each other. Maximum number of point of intersection of three lines on a plene is three.

What is the maximum number of regions a plane can divide?

One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions, and so on. When the n th line is added to a cluster of (n-1) lines then the maximum number of extra regions formed is equal to n.

How many regions can be obtained from two lines?

This is because, if we want to obtain the maximum possible number of regions, we shall not let the new line pass through the intersection of the first two, for then we would get six regions and can do better.

How many regions does a plane divided by two parallel lines divide?

Two straight lines (parallel to each other) divides the plane into 3 regions, and so on. n straight lines (parallel) divides the plane into n+1 regions. 8 clever moves when you have $1,000 in the bank.

How many straight lines can divide a plane into 2?

One straight line can divide a plane into 2. Two straight lines can divide a plane into 4. Three straight lines can divide a plane into 7. observe the sequence: 2, 4, 7,….