question for math lovers

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Anonymous
question for math lovers 2017-07-23 09:47:32 Post No. 9057979
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question for math lovers Anonymous 2017-07-23 09:47:32 Post No. 9057979 [Report]

hey guys, today I had a thought - "if you have 4 circles such that every two cricles have an overlapping region, then that overlapping region also has to be the overlapping region of all four circles (meaning, all 4 circles necessarily overlap at some region).
This was just a hunch, but I wanted to know if any of you can prove it true (I'm completely unqualified to even try). If it is - please explain why. If not - same thing (and try figuring what is the maximum number of circles that can still fit these criteria, if such a number exists).
Just to make things clear - this problem is strictly 2-dimensional.

Cheers and thanks.

Anonymous 2017-07-23 11:07:29 Post No.9058128
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Anonymous 2017-07-23 11:07:29 Post No.9058128 [Report]

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>>9057979
I don't think your hunch is correct.

Anonymous 2017-07-24 09:43:12 Post No.9059217
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Anonymous 2017-07-24 09:43:12 Post No.9059217 [Report]

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>>9058128
dang it I forgot to mention the most important condition - no circle can completely contain one or more of the other circles (I kind of missed the punch line haha)

Anonymous 2017-07-24 12:04:01 Post No.9059353
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Anonymous 2017-07-24 12:04:01 Post No.9059353 [Report]

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Thissss works rightt??

Anonymous 2017-07-24 12:26:36 Post No.9059376
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Anonymous 2017-07-24 12:26:36 Post No.9059376 [Report]

>>9059353
is a similar solution possible for any number of circles?

Anonymous 2017-07-24 01:06:57 Post No.9059417
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Anonymous 2017-07-24 01:06:57 Post No.9059417 [Report]

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>>9059376
Yes but it's trivial.

Anonymous 2017-07-24 01:31:49 Post No.9059435
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Anonymous 2017-07-24 01:31:49 Post No.9059435 [Report]

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There's a Venn Diagram which has every combination of overlaps to represent logical distinctions. It's a subtype of Euler diagram.

>>9059217
A Venn diagram has the additional constraint of each area having an area of no overlap.

As I recall any number of overlaps is possible, but I'm not sure if they can keep being circles. Check wikipedia.

Anonymous 2017-07-24 03:50:30 Post No.9059675
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Anonymous 2017-07-24 03:50:30 Post No.9059675 [Report]

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trivial..got it?

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I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible.
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