Subject:
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Re: Pythagorean Triads and Almost-Triads
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Newsgroups:
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lugnet.build
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Date:
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Fri, 21 Jan 2000 02:01:47 GMT
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Viewed:
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628 times
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John J. Ladasky Jr. wrote in message <38814540.ED2D820E@my-deja.com>...
> Geez, Paul,
>
> This is the second time I've bumped into you ,doing a project identical
> to one of mine! (The other one was the 3-D map of nearby stars, in case
> you've forgotten.)
John, how could I possibly have forgotten that? ;-)
> I think that you want to measure your error margin as a fraction of the
> total hypotenuse length, rather than as the absolute number of studs.
>
Here we go again..... :-)
I think I don't. You see, my rule of thumb is that the walls that form the
sides of the triangle will not be absorbing ANY deformation stress, because
their thickness and construction are unknown (i.e. dependent entirely on the
modeller's application). I worked by the assumption that the
hinges/technic-pegs will be absorbing the deformation stress, and last time
I looked, that was a constant for all triangles I examined, that is, three
("3") :-) Therefore, my error margin turns out to be constant too. Neat,
huh? ;-)
>
> My chart differs from Paul's in several ways:
>
> 1) All entries are ordered by the smallest angle.
Who was it said something about "pasting these tables into a spreadsheet"?
Oh, that's right, it was both of us :-)
> 2) I've included possible HALF-stud entries, for those of you who use
> offset plates. I've been experimenting with this, and it looks
> promising.
>
> 3) My table only includes a few entries where either x or y exceeds 20
> studs. There were practical reasons for stopping here, both computer • [...]
>
> 4) For the standard angle plates (did I miss any?), I have listed some
> entries where the rise and run corresponding to the angled edge are both
> whole numbers, but for which the strain is too high. The reason for
> this is to emphasize the first entry that IS usable. For example, take
What kind of a reason is that? Put in the entries that ARE useable and they
emphasise themselves. Unusable ones just clutter up the table.
Oh, and another difference is:
5) It contains redundant multiples. I always assumed that people could
trivially extrapolate to find these, and would only want the fundamental
triads... silly me :-)
>
> Now, consider that we've only talked about angles in the plane defined
> by studs. But what about tilting a wall up in the vertical direction?
> You can build such walls using Technic pegs, or with 1 X 2 hinge bricks.
> What dimensions are permissible? I'm still working on the practical
> aspects of this, though I have a table of theoretically-acceptable
> triangles. I suspect that the strain permitted in the vertical-plane
> triangles will not be as high as in the horizontal-plane triangles.
I suggest that you assume that the sides accept no strain, and limit the
strain to that accepted by the joints, as above. Otherwise people are going
to spend a lot of time having to build stuff that they're not sure will
work, simply because their sides are built slightly differently. This
greatly limits the usefulness of the table, which was meant to save time
(IMO). Then again, your table already contains a lot of data that is either
redundant or not actually useable. I also, therefore, suggest that any
triads for which the strain is outside limits but still possibly useable
(depending on construction) be put in a separate table for people to resort
to if there are no acceptable "strict" solutions.
It's rather ironic, when we were debating error margins on star maps, _you_
were the one who was suggesting my error limits weren't strict enough. Now,
the tables seem to have turned. Funny, eh? Still, we live and learn ;-)
> So, since you're a Space fan like me, I have to wonder whether I'll
> finish my wedge-shaped spacecraft before you do... are you married?
> Does your wife have the flu? How about your kid? This year's strain of
> influenza routinely incapacitates healthy adults for over seven days.
> Needless to say, I'm not getting much done this week...
Well, the next task for one of us is to tackle what is probably a greater pr
oblem, where 3 (or more, but 3 is a good start) of ANY triangle each share a
common side and all their sides must be integers (within error). If people
are building with hinges/pegs they need not merely be incorporating single
right-angled triangles into conventional orthogonal constructions. I, for
one, would like to know what arbitrary triangles I should choose if I want
them to each share a side with each other (and connect up properly with
integral stud lengths).
Paul
http://www.geocities.com/Area51/Shuttle/5168/
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Message has 1 Reply:
 | | Re: Pythagorean Triads and Almost-Triads
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| (...) Oh great, another one of our geeky debates! 8^) (...) Do we know this for a fact? The LEGO hinge bricks are pretty snug. The joint is a Technic peg, but it is fixed to one brick. And you can't even disassemble the hinge plates. In spite of (...) (24 years ago, 21-Jan-00, to lugnet.build)
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Message is in Reply To:
| | Re: Pythagorean Triads and Almost-Triads
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| Geez, Paul, This is the second time I've bumped into you ,doing a project identical to one of mine! (The other one was the 3-D map of nearby stars, in case you've forgotten.) (...) Emerging from my LEGO Dark Ages last fall, we opened an Exploriens (...) (24 years ago, 16-Jan-00, to lugnet.build)
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