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# A pentagon in a pentagon in a pentagon

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Posted 22 February 2013 - 05:42 AM

Conjecture: As long as each of the two smaller pentagons are formed by joining the midpoints of the next larger pentagon, the two ratios of the areas will always be equal and the two ratios of the perimeters will always be equal, no matter what shape the largest pentagon has.

Under what conditions is this true?

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### #2 bonanova

bonanova

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Posted 22 February 2013 - 05:54 AM

Conjecture: By saying "whatever shape the pentagon has" you are not limiting the discussion to regular pentagons.

True?

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Vidi vici veni.

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Posted 22 February 2013 - 05:56 AM

Conjecture: By saying "whatever shape the pentagon has" you are not limiting the discussion to regular pentagons.

True?

yes.  any pentagon

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### #4 bonanova

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Posted 22 February 2013 - 06:46 AM

Spoiler for Looks like

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Vidi vici veni.

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Posted 22 February 2013 - 01:41 PM

Spoiler for Looks like

Not all them.
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### #6 bonanova

bonanova

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Posted 23 February 2013 - 09:47 PM

Spoiler for Looks like

Not all them.

I'm not making any progress. Any tips for analyzing this?

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Vidi vici veni.

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Posted 24 February 2013 - 12:39 AM

Spoiler for help

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Posted 25 February 2013 - 01:00 AM

Spoiler for help

Spoiler for help2

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