Polygons

Oct. 7th, 2007 at 3:55 PM

When I am not posting to my livejournal, I often think about odd mathematical problems. Such as, For any polygon with more than 4 sides, is it possible to draw a rectangle inside it such that each vertex touches an edge of the polygon, and no two vertices are on the same edge?

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( 8 comments — Leave a comment )

eds3

Oct. 8th, 2007 04:42 pm (UTC)

Me, too!

I have a similar affliction. Earlier today I was walking toward the vending machine with a large number of coins. I wondered which was the optimum transaction for a $0.40 purchase- 1 quarter, 1 dime, 1 nickel, or 4 dimes, or 2 quarters with 1 dime as change. Then I began wondering what I meant by "optimum." Am I optimizing for weight, for fit in my pockets, or for ability to make change later?

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kevin_hogan

Oct. 9th, 2007 03:01 am (UTC)

Re: Me, too!

Optimum, of course, is the minimum transaction which uses no quarters and returns all quarters as change - because everyone knows that quarters are the most useful coins!

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grieve

Oct. 11th, 2007 01:40 am (UTC)

Re: Me, too!

I thought optimum was fewest coins with highest symmetry, so 2 quarters with 2 nickels change would be optimal. :)

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kevin_hogan

Oct. 11th, 2007 01:54 am (UTC)

Re: Me, too!

You obviously don't do your laundry with a coin-op washer ;)

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grieve