# Circle axioms

#### shaharhas

##### New member
On what Axioms that concern in this question are based:
What the maximal number of regions that a state that 3 circles that intersect together?

#### MarkFL

##### Super Moderator
Staff member
Here is a configuration with 7 areas:

Can you think of any adjustment we can make to create more than 7 areas?

#### Dr.Peterson

##### Elite Member
On what Axioms that concern in this question are based:
What the maximal number of regions that a state that 3 circles that intersect together?
I'm not sure what sort of axioms you are looking for. Are you thinking of geometry or combinatorics or something else?

Also, as I see it, three circles form 8 regions, including the exterior, so you need to clearly state what you mean by that.

#### shahar

##### Junior Member
two links of two sites that concern in the two topic would be helpful!
the topics = combinatorics & geometry.
Especially, in geometry.

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#### shahar

##### Junior Member
You can start with a trial and error strategy, and later on
Reach the conclusion that the maximum number of domains is
7, when the conclusion can be reinforced on the following grounds: creation
The greatest possible number of domains involves multiple points
The largest intersection between the three circles. So in fact
We must create a situation in which every two circles are cut between them
In two points, and there is no situation where three circles are cut
At one point.
One of the possible situations is shown in Figure 1 (The picture above) and contains 7
Different areas.

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#### shahar

##### Junior Member
I'm not sure what sort of axioms you are looking for. Are you thinking of geometry or combinatorics or something else?

Also, as I see it, three circles form 8 regions, including the exterior, so you need to clearly state what you mean by that.
Why 8?
Can you explain?

#### pka

##### Elite Member
Why 8?
Can you explain?
There are seven bounded areas and one unbounded area( outside the seven).

#### Denis

##### Senior Member
Why did you post 1st post under shaharhas ?

Have a look at this sequence:

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#### Denis

##### Senior Member
There are seven bounded areas and one unbounded area( outside the seven).
But if you draw a rectangle around the intersecting circles
such that each side of the rectangle is tangent to a circle,
then you get 4 more areas and no annoying unbounded area

#### topsquark

##### Full Member
But if you draw a rectangle around the intersecting circles
such that each side of the rectangle is tangent to a circle,
then you get 4 more areas and no annoying unbounded area
Still having problems counting to five are you? Take a look again.

-Dan

#### Denis

##### Senior Member
Still having problems counting to five are you? Take a look again.
Yer right....missed the sungun at bottom-center

#### Jomo

##### Elite Member
Denis, you made another mistake. Are you still drinking that Canadian water?

#### Otis

##### Senior Member
… if you draw a rectangle around the intersecting circles … then you get … no annoying unbounded area
What about the area outside the rectangle?

#### Denis

##### Senior Member
What about the area outside the rectangle?

That area is VERY large

#### Otis

##### Senior Member
That area is VERY large
Indeed! That's why we call it an "unbounded area".

(Hope yer not still a noid.)

#### Denis

##### Senior Member
Grade 1 session; teacher draws 2 circles on blackboard...
teacher: class, how many areas have I created?
li'l Suzy Q: two
teacher: correct Suzy
li'l Johnny: no...that's 3 areas; 2 bounded and 1 unbounded!
teacher (secretly googles "unbounded area" and turns red!): correct Johnny