plainglazed
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Posts posted by plainglazed
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color me Purple
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Spoiler for a guess
one, only
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I'm game. I check in at least daily. Don't always sign in tho.
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Spoiler for some supporting math
I have the same calculations as DejMar but with an assumption that I cannot yet prove yields a minimum web length. In my last response I thought this problem must have some grand symmetry and assumed the red lines in my drawing (above) must be the same distance x from their nearest two sides of the cube described by the eight corks. The following assumes a magical 30 degree angle of those red lines:
f(x) = 8/sqrt(3) + 4(1-2x)/sqrt(3) + 1-2sqrt(1/12-x2)-(1-2x)/sqrt(3)
f(x) = 8/sqrt(3) + 3(1-2x)/sqrt(3) + 1-2sqrt(1/12-x2)
f(x) = 8/sqrt(3) + sqrt(3)(1-2x) + 1-2sqrt(1/12-x2)
f'(x) = -2sqrt(3) + 2x/sqrt(1/12-x2)
f'(x) = 0 when x = .25f(x=.25) = 1+9/sqrt(3) ≈ 6.196
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Hmm, let's put the axes of the trapezae on each of two motorized pinions which would travel the full length of each of two racks in the time the swinger travelled from platform one to trapeze two or from trapeze two to platform two. Assuming the length of each rack is infinity/2, the platforms could be infinity apart.
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adding Bb3k's headless stick figure and crunching some numbers:
8(2x2+.52).5+ 4(1-2x)/3.5+ 1-2x-(1-2x)/3.5
f(x) = 8(2x2+1/4).5 + 3(1-2x)/3.5 + 1–2x
f’(x) = 16x/(2x2+1/4).5 – 2(3.5) – 2
f’(x) = 0 when x = ~.195
f(x=.195) = 4.568 + 1.409 + .258 = 6.235
the sqrt(3) comes from TSLF's 2D connect the dots:
f(x) = 4(x2+.52).5 + 1 – 2x
f”(x) = 4x/(x2+1/4).5 – 2
f’(x) = 0 when x = 1/2(3.5) = ~.289
tan-1(1/2(3.5)/.5) or tan-1(1/3.5) = 30°
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and a Spoiler for some additional thoughts:
I think 1/sqrt3 is more likely than e. Bb3k's described improvement to tojo982's offering: "The left and right side of the X's are pushed inward to make a 0.5 mile road in the middle." If we vary the .5 mile connection, we can generalize the length of this path:
4sqrt(.52 + (.5tan(a))2) + 1-tan(a)
where (a) is the angle formed by the y-axis and the X in Bb3k's drawing above. This expression minimizes when (a) is 30 degrees.
EDIT: although now I'm not so sure. don't know if the rounding in Excel or my calculator is more accurate and the kind of calculus needed here i've long since forgotten. really quite amazing that the two are so close. in any event, Bb3k's answer I thought was quite clever and satisfied the OP.
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Spoiler for one calculation
using nine segments of equal length yields 3(10.5 - 1) or ~6.4868
That is if my math holds up.
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without getting too political, what I meant was, just as the word spouse can mean either one, so does the parallel term in the answer.
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Don't think it could ever be possible
for a raw egg to crack a concrete floor
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Hey hey you two - Wilson, know it's been a while since you posted the above but gotta say, very clever as always - indeed too clever for me. And just reviewed these and only now do I fully get your previous stab at this one. Always been fifty fifty on the spelling of that arid wasteland or after meal treat. Love it.
T - thanks for the bump. All's true in your spoiler above with the exception that the spouse is not gender specific.
Cheers
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perhaps...
Spoilerthe room was a bakery, or deli, or butcher, or the like with one of these:
so the friend outside heard the baker yell the number before his friend inside rang the bell to be served???
urghh - was right there. darn pesky work thing.
Re-ROLLO
in Games
Posted
OK, see now editing is no good.
HEART
if 1 then T is last: first two are BU and not AR from BOARD - 1