- Thread starter shaharhas
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I'm not sure what sort ofOn whatAxiomsthat concern in this question are based:

What themaximal numberof regions that a state that 3 circles that intersect together?

Answer: the number is 7.

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

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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.

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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Why 8?I'm not sure what sort ofaxiomsyou are looking for. Are you thinking of geometry or combinatorics or something else?

Also, as I see it, three circles form8 regions,including the exterior, so you need to clearly state what you mean by that.

Can you explain?

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There are seven bounded areas and one unbounded area( outside the seven).Why 8?

Can you explain?

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But if you draw a rectangle around the intersecting circlesThere are seven bounded areas and one unbounded area( outside the seven).

such that each side of the rectangle is tangent to a circle,

then you get 4 more areas and no annoying unbounded area

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Still having problems counting to five are you? Take a look again.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

-Dan

Yer right....missed the sungun at bottom-centerStill having problems counting to five are you? Take a look again.

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

That area is VERY largeWhat about the area outside the rectangle?

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

(Hope yer not still a noid.)

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