Subject:
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Pythagoras and his triangles and building
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Newsgroups:
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lugnet.technic
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Date:
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Wed, 21 May 2008 16:51:15 GMT
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Viewed:
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13402 times
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Hi all,
If you are like me, you like to make things sturdy when you build them. One way
to do this is to build cross links. Putting things at angles other than 90
degrees is helpful, but then you need to know some Pythagorean triples to do the
trick.
I keep in my head three Pythagorean triples: 3-4-5, 5-12-13, and 7-24-25. Of
course, all of these can be modified by multiplying by a constant, so they are
not nearly as limiting as they might appear.
Now, when I put support braces on things, I count and look for multiples of 3 or
4 or 5 or 12 or 7 or 24 so that I can use the triples that I know. And then I
get all confused because I tend to do the math in my head and three plates
equals one block and six studs equals five blocks and five plates equals two
studs and ... Aggh! I'm so confused!!
So, a friend of mine wrote a webpage that gives Pythagorean triples. You just
give it a number and it gives you all the primitive triples that use that
number. I told him that it was pretty neat but I wanted _all_ the triples, not
just the primitive ones and I also needed all the ones _near_ a certain number,
since I might be able to put the support point at any number of points near the
top of the tower.
So, he changed the code to do all that. What a good friend!
Example: you are building a Lego technic thing that is going to be about 45
blocks high and you want to put a triangular support onto it, to keep it
vertical and stable. So you need a Pythagorean triple that has numbers near 45
in it. Well, go to his Pythagorean Triples Finder page
<http://data.vanderbilt.edu/~koyamat/brew/pythagoras.html> and enter in the
number 36 into the box and it will give you all the Pythagorean triples that
contain 36, then all those that contain 37, then all those that contain 38, ...
, and finally all those that contain 45.
So, you can say, "Hmmmm, I want to put the support peg at 42 bricks from the
top, so I can use the 40-42-58 or the 42-56-70 right triangle." (You could also
use the 42-144-150 or the 42-440-442 but that takes lots more parts.)
Oh, your design needs to change and the support needs to be at 40 instead of 42
beacuse the motor is being attached there? No problem, there are 8 Pythagorean
triples that have 40 in them.
As a side benefit, it will tell you which of those numbers are prime, just in
case you needed a prime number finder too!
Happy reinforcementizing!
Rafe
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