Circle axioms

shaharhas

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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?
Answer: the number is 7.
 

MarkFL

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Here is a configuration with 7 areas:

11301

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

Dr.Peterson

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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?
Answer: the number is 7.
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

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two links of two sites that concern in the two topic would be helpful!
the topics = combinatorics & geometry.
Especially, in geometry.
The source with the answer (The Answer 7):
Thanks, in advance!!!
 
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shahar

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Google Translate:
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

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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

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Denis

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Why did you post 1st post under shaharhas ?

Have a look at this sequence:
 
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Denis

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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

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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

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Jomo

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

Otis

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

😕
 

Denis

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Otis

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Denis

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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 :(
 
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