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Author Topic: CHALLENGE : Rectangles  (Read 21963 times)

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deegeecees

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Re: CHALLENGE : Rectangles
« Reply #60 on: September 28, 2006, 02:15:06 PM »
Quote from: Greg B on September 28, 2006, 01:24:13 PM
Geeks!

 :grazy:

Naw, I just think funny is as funny does, and I know from funny. Like this memorable quote:

Squad Leader: "Stay on target"
Porkins: "Their coming in too fast!"
Squad Leader: "Stay on target"
Porkins: "I caaant see em!"
Squad Leader: "Stay on target"
Porkins: "Whaaaaaa......"
Squad Leader: "We lost Porkins"


Poor Porkins.
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Greg B

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Re: CHALLENGE : Rectangles
« Reply #61 on: September 28, 2006, 05:14:16 PM »
How about?
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Kerry

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Re: CHALLENGE : Rectangles
« Reply #62 on: September 28, 2006, 05:40:17 PM »
solo, welcome to the swamp ... ignore the comments from the peanut gallery. :lol:  someone let them out of their cage ..

now that you are logged in you can probably see the place where they usually live.

//// back on topic ..

If 'anyone' < points finger at you> can devise a solution that resolves this in one pass I'd be really interested in seeing it.
 
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kdub, kdub_nz in other timelines.
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sinc

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Re: CHALLENGE : Rectangles
« Reply #63 on: September 28, 2006, 06:26:13 PM »
Quote from: Kerry Brown on September 28, 2006, 05:40:17 PM

If 'anyone' < points finger at you> can devise a solution that resolves this in one pass I'd be really interested in seeing it.
 

I came up with a couple of different formulas for solving the problem in one pass, but they both ended up being complicated differential equations.  If there's a way to solve them symbolically, I either can't remember it or can't see it.  I haven't really done much of this stuff since college, fifteen-odd years ago...  The numerical solution is definitely easier, if you have a computer.
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SEANT

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Re: CHALLENGE : Rectangles
« Reply #64 on: September 29, 2006, 07:15:07 AM »
I am also "Vexed" by this problem.  In the spirit of collaboration (and in the interest of giving my mind a rest) here's a contribution to a possible solution.

The only concrete thing I have is the equation to find the "Shortest Hypotenuse" rectangle for a given hole (see also attached .xls).  This rectangle has the unique properties of a hypotenuse equal to Hole length, corners at 1/2 height of Hole rectangle, , 1/2 Area of Hole rectangle Area.  Another interesting property is A x B = (1/2H)2.

With any luck this info will shake out some new ideas.

Sean

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Sean Tessier
AutoCAD 2016 Mechanical

CADaver

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Re: CHALLENGE : Rectangles
« Reply #65 on: September 29, 2006, 08:07:19 AM »
Bear in mind that all the resultant triangles are "similar triangles" whose sides would be ratio related.
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Swift

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Re: CHALLENGE : Rectangles
« Reply #66 on: September 29, 2006, 08:19:14 AM »
Seant Welcome Aboard and thanks for the contribution!

Now:
Your excel sheets and equation give a result which is significantly different than ours. I thought it would have been a unique solution, eh back to the scratchpad
« Last Edit: September 29, 2006, 08:30:18 AM by Swift »
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Swift

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Re: CHALLENGE : Rectangles
« Reply #67 on: September 29, 2006, 08:33:17 AM »
Seant,

Draw your solution out. Using the side lengths I got from your spreadsheet the interior angles of the interior polygon are not 90.
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solo

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Re: CHALLENGE : Rectangles
« Reply #68 on: September 29, 2006, 10:51:55 AM »
Hi CADaver,

You're right.  The resultant triangles will be similar but we do not know enough info about them to determine the direct relationship between them.  Only having one side of the triangle and no angle makes it really difficult to determine a sure fire formula that will work for any peg size and hole size combination.

I can create a relationship but it's a relationship of unknowns so i can't derive an answer.  At this point i am trigonometrically bankrupt.  I used to have a TI-82 graphing calculator that i thought was capable of calculating a formula based on an XY list.  I thought i might be able to enter numbers from tested dimensions from differant conditions and create a formula that would be close enough (if not exact) to see what's going on.

Solo
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SEANT

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Re: CHALLENGE : Rectangles
« Reply #69 on: September 29, 2006, 05:51:03 PM »
I should have taken more time to explain what I was posting. 

In the search to find a general math solution to the original challenge this was one of only two sized pegs for the given size hole I was certain about . A perfect match, and a rectangle that had a hypotenuse equal to the hole length.  It is not a solution for the target depth of 200, but the spreadsheet does give the dimensions of a "Shortest Hypotenuse Rectangle" for any Rectangle Hole size.

I'm unsure if this will have any bearing on an "ultimate" math solution, if there even is one, but it does illustrate some know relationship.  I suspect it will require the use of all of the knowns (there aren't many) to come up with a solution.

I also see that my GIF image was truncated.  Let's hope I get better with subsequent posts.

Sean

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Sean Tessier
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SEANT

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Re: CHALLENGE : Rectangles
« Reply #70 on: September 29, 2006, 06:05:36 PM »
Apparently the GIF image may or may not be truncated based on the aspect ratio of a monitor.  Imagine rectangles of different size giving me fits like that. :?

If anyone cares to see the full image, or, for that matter, would like to see how this equation was derived, please ask.
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Sean Tessier
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Kerry

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Re: CHALLENGE : Rectangles
« Reply #71 on: September 29, 2006, 06:14:14 PM »
SEANT, the gif looks fine to me.



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kdub, kdub_nz in other timelines.
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Kerry

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Re: CHALLENGE : Rectangles
« Reply #72 on: September 29, 2006, 06:15:44 PM »
... and yes, I'd like to see how it was derived.
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kdub, kdub_nz in other timelines.
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SEANT

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Re: CHALLENGE : Rectangles
« Reply #73 on: September 29, 2006, 08:56:14 PM »
There is a typo in the equation of my first post: Should read -4(H/2)2. 

I'm living up to my mosquito ranking.  Fortunately, the spreadsheet is working as expected.

See attached PDF for updated scratch sheet. 

Sean
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Sean Tessier
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Kerry

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Re: CHALLENGE : Rectangles
« Reply #74 on: September 29, 2006, 09:16:25 PM »
Thanks SEANT,

I'll have a look at that tonight.  I'm having trouble visualising the application of Shortest Hypotenuse derivitaves to this problem ... but thats my issue :-)


You know, of course, that the 'Mosquito' has nothing to do with your presumed talent ... just an indicator of your posting count. 

:lol: < deleted references to the natural reverse corollary of your assumption >
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kdub, kdub_nz in other timelines.
Perfection is not optional.
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