Table of Contents
- 1 What is the maximum number of regions you can have with N chords in a circle?
- 2 What is the maximum number of regions that three chords of a circle could divide the circle into?
- 3 What is the maximum number of parts a circle can be divided?
- 4 How many regions does a circle divided by 4 divide into?
- 5 What happens when you divide a circle by 2 points?
What is the maximum number of regions you can have with N chords in a circle?
If we pick three distinct points on a circle and connect each pair of them with a chord, we can form four distinct, nonintersecting regions.
What is the maximum number of parts a circle can be divided by drawing nine straight lines?
The answer is 22.
What is the maximum number of non overlapping regions that can be determined by three lines in a plane?
7 regions
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.
What is the maximum number of regions that three chords of a circle could divide the circle into?
6 is the maximum number of regions that three chords of a circle could divide the circle into?
How many parts can a circle be divided into?
A circle is divided into 12 equal parts.
How many regions are there in a 7 point circle?
57 regions
If we add a 7th point, and count very carefully, we get 57 regions.
What is the maximum number of parts a circle can be divided?
Using five lines, circle can be divided into sixteen parts.
What is the largest number of parts that can be obtained from cutting a circle using 5 straight cuts?
If you cut it with FIVE straight lines you get a maximum of SIXTEEN bits.
What is the maximum number of regions possible?
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).
How many regions does a circle divided by 4 divide into?
In the figure you can see the dark lines connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8).
How many chords are on a circle with 7 points?
It should be clear that there should be 6 chords at every point on the circle, because we are connecting every point with every other point, except itself. So for 7 points there are
When is the number of regions of a circle maximal?
The lemma asserts that the number of regions is maximal if all “inner” intersections of chords are simple (exactly two chords pass through each point of intersection in the interior). This will be the case if the points on the circle are chosen ” in general position “.
What happens when you divide a circle by 2 points?
However, it seems like 2 points divide the circle into 2 areas, 3 into 4, 4 into 8, 5 into 16, and so the pattern keeps working. Here is what happens for n = 6 : Let’s draw a circle with points a 1, a 2, a 3, a 4 and a 5. Now put a 6, without loss of generality, between a 1 and a 5.