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Author Topic: CHALLENGE : Rectangles  (Read 21653 times)

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Kerry

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CHALLENGE : Rectangles
« on: September 21, 2006, 04:09:49 AM »
It's been a while since we've had a challenge, so ...

CHALLENGE : Rectangle pegs in Rectangular holes ..

Provide geometry proof or code to determine the length of a rectangular shape to fit into a rectangular hole as shown :-

Assume
Shape depth = 200
Opening Height = 500
Opening Width = 1000

Enjoy .. :-)

/// kwb
« Last Edit: September 21, 2006, 04:11:42 AM by Kerry Brown »
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kdub, kdub_nz in other timelines.
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Everything will work just as you expect it to, unless your expectations are incorrect.
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Jeff_M

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Re: CHALLENGE : Rectangles
« Reply #1 on: September 21, 2006, 04:25:28 AM »
Sure! Throw this up when I should be sleeping! No code for me tonight, and all the 'other' swampers in other time zones will see it before I wake...<sigh>
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Kerry

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Re: CHALLENGE : Rectangles
« Reply #2 on: September 21, 2006, 04:27:37 AM »
Sorry Jeff ... It may still  be unresolved when you wake ...  so don't lose any sleep over it :-)
« Last Edit: September 21, 2006, 04:28:45 AM by Kerry Brown »
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kdub, kdub_nz in other timelines.
Perfection is not optional.
Everything will work just as you expect it to, unless your expectations are incorrect.
Discipline: None at all.

David Hall

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Re: CHALLENGE : Rectangles
« Reply #3 on: September 21, 2006, 10:01:41 AM »
Its to early for TRIG Kerry, neeed moooorrre   coffeeeeeee
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Sometimes the question is more important than the answer. (Thanks Kerry for reminding me)

T.Willey

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Re: CHALLENGE : Rectangles
« Reply #4 on: September 21, 2006, 11:32:17 AM »
Had this challenge over on the Adesk Ng, no one solved it, as far as I remember.  See if I can find the link.
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Tim

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LE

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Re: CHALLENGE : Rectangles
« Reply #5 on: September 21, 2006, 11:34:08 AM »
Quote from: T.Willey on September 21, 2006, 11:32:17 AM
Had this challenge over on the Adesk Ng, no one solved it, as far as I remember.  See if I can find the link.

Asi es.... I think Joe Burke provided a solution.
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T.Willey

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Re: CHALLENGE : Rectangles
« Reply #6 on: September 21, 2006, 11:37:35 AM »
Quote from: LE on September 21, 2006, 11:34:08 AM
Quote from: T.Willey on September 21, 2006, 11:32:17 AM
Had this challenge over on the Adesk Ng, no one solved it, as far as I remember.  See if I can find the link.

Asi es.... I think Joe Burke provided a solution.
I think you might be right Luis.  I think he didn't like it though because it was using a testing method, and not a real math soloution.

Well here is the link.
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Tim

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Greg B

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Re: CHALLENGE : Rectangles
« Reply #7 on: September 21, 2006, 12:15:39 PM »
x=opening width
y=opening height
z=shape depth

find w = shape width
If x=1000 then
w = x-y
(w = 1000-500)

w = 500


You just asked for it to fit in the rectangluar hole.... :wink:
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Jeff_M

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Re: CHALLENGE : Rectangles
« Reply #8 on: September 21, 2006, 03:11:56 PM »
Quote from: Greg (MCMLXXIV) on September 21, 2006, 12:15:39 PM
You just asked for it to fit in the rectangluar hole.... :wink:
Maybe you missed the "as shown" part? :)
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Kate M

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Re: CHALLENGE : Rectangles
« Reply #9 on: September 21, 2006, 03:19:32 PM »
I'm pretty sure this requires differential equations to get a real solution -- I wrote a system of equations, and it appears to be a second-order problem. If I feel like dragging out an old textbook maybe I'll give it a shot.  :roll:
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Greg B

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Re: CHALLENGE : Rectangles
« Reply #10 on: September 21, 2006, 03:35:27 PM »
Quote from: Jeff_M on September 21, 2006, 03:11:56 PM
Quote from: Greg (MCMLXXIV) on September 21, 2006, 12:15:39 PM
You just asked for it to fit in the rectangluar hole.... :wink:
Maybe you missed the "as shown" part? :)

First rule of drafting...

Numbers come first, the way the drawing looks comes second.
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Bob Garner

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Re: CHALLENGE : Rectangles
« Reply #11 on: September 21, 2006, 04:03:25 PM »
I once had to develop equations for moving the largest rectangle between two walls and around a corner, somewhat like this puzzle.  I don't remember the solution but I remember it was based on the diagonal dimension of the inner rectangle.  Find the diagonal in one direction, it has to be equal and opposite in the other direction (mirrored?).  The rest is basic trig.

I'm busy trying to figure out some new concrete design equations today, so I don't want to even try to figgur this out.
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Swift

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Re: CHALLENGE : Rectangles
« Reply #12 on: September 21, 2006, 05:53:21 PM »
I have it sketched out on my board at the office. I think Kate is right it would require calculus to solve explicitly, but I think I have it worked out where it can be solved using linear algebra. I plan on spending more time on it once I get home.
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David Hall

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Re: CHALLENGE : Rectangles
« Reply #13 on: September 21, 2006, 11:06:09 PM »
I have the equation worked out where y is solved in terms of x .  I'll try and post a pic of the equation.  Tomorrow, I will see if I can get an answer
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Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second.
Sometimes the question is more important than the answer. (Thanks Kerry for reminding me)

David Hall

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Re: CHALLENGE : Rectangles
« Reply #14 on: September 21, 2006, 11:13:41 PM »
I got
(200)^2 = (500- X1)^2 + (1000 - Y1)^2
40000 = 250000 - 1000X1 + (X1)^2 + (1000 - Y1)^2
-210000 - (1000 - Y1)^2 = -1000X1 + X1^2
X = SQRT(-Y^2 + 1000Y -210000) + 1000
« Last Edit: September 22, 2006, 10:02:19 AM by CmdrDuh »
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Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second.
Sometimes the question is more important than the answer. (Thanks Kerry for reminding me)
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