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aeh5040

Eurobricks Knights
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Everything posted by aeh5040

  1. aeh5040
    Sure, I'll see what I can do. The construction itself is pretty simple - it's mostly just a very very rigid box...
  2. aeh5040
    I agree - these are very useful and interesting constructions. This very interesting article is somewhat related (it is about Meccano, but it works just as well with Lego liftarms). Among other things, it shows how to perfectly brace a regular pentagon. http://www.staff.science.uu.nl/~hooft101/lectures/meccano.pdf
  3. aeh5040
    You wouldn't say that if you saw all the failed prototypes!
  4. aeh5040
    Check out: http://brickset.com/article/23288 and:
  5. aeh5040
    Thank you for the kind remarks! That's right. Yes, that would give a different (but related) melody. In change ringing terminology it would give a different course of plain hunt. Cool! I was wondering if I would find anyone else who shares both hobbies! I'm curious to know whether you find the demo at all helpful (rather than merely amusing). E.g., one can try to watch two coursing bells, say the 8 (red) and the 7 (orange), to see how one follows the other down to lead. Yes, plain hunt on 7 with a cover would be possible. It would need either a separate carousel for the tenor, or another "layer" of pegs, around the outside say. In principle it would be possible to ring other methods such as plain bob, using multiple carousels rotating at different speeds. The required precision would likely make it impractical, though. Yes. They also serve the important function of making the hammer spring away from the bell immediately after the strike, otherwise it would deaden the sound.
  6. aeh5040
    Here is my latest creation. It rings "plain hunt on eight", a traditional change ringing method originating in 17th century England, on eight toy handbells (the only non-Lego parts). Yes, I am nuts. Enjoy!
  7. aeh5040
    My guess is that the presence of the smaller box is supposed to add some strength to the outer box. And possibly to prevent all the bags piling up at one end and damaging the outer box. But it does seem like a strange approach.
  8. aeh5040
    Can you explain why? Surely the gear ratios depend on the gear combinations used, not how they are distributed between axles...
  9. aeh5040
    Cool! To me it really is a slightly new way of looking at why Pythagoras works (although doubtless many people have been there before). As it happens I did notice essentially the same phenomenon a few months ago by looking at two trans-clear base plates, as shown below, so I was primed to notice the significance of your construction. So this really is an example of a (minor) mathematical insight from Lego!
  10. aeh5040
    It's certainly not impossible! One way would be a groove cam like akiyuky's controlling each driving ring, but with three positions. However, a compact reliable solution seems unlikely, whereas redesigning the gearbox itself is relatively straightforward.
  11. aeh5040
    That would be much easier. What he is asking for is for each driving ring to execute the sequence FROOOO.
  12. aeh5040
    I would not be optimistic about a compact solution to this, unfortunately. I think you might be better off redesigning the gearbox so that the gears come in a different order, such as: FOO, OFO, OOF, DOO, ODO, OOD
  13. aeh5040
    I'm afraid you're still showcasing and not proving the theorem. There is a common misconception that pictures cannot yield proofs, but in this case your fear is misplaced. The construction definitely gives a fully rigorous proof, and in fact it even extends to the general case of Pythagoras' theorem. Filling in some details: Consider two congruent right-triangles ABC and BCD with shorter sides 1 and 2 and sharing a hypotenuse. Add two further right-triangles CDE and CEF, congruent to each other, with shorter sides 2 and 4 and sharing a hypotenuse, as shown. Since all four triangles are similar, ACF are collinear. Finally, drop the perpendicular BG. Then triangle EGB is right-angled and has sides 4-1=3, 2+2=4, and 4+1=5. Similarly, starting with AB=x, AC=xy, DE=x y^2 gives the general Pythagoras theorem after a bit of algebra. It's interesting that the same construction also proves the tangent double-angle formula (again in a special case, which is easily generalized): tan <FEC = 1/2; tan (2 <FEC) = tan <FED = 4/3.
  14. aeh5040
    That was a very interesting and thorough investigation. (I don't think I've ever seen a Lego part that close up!) I hope you get it sorted...
  15. aeh5040
    Taking this a bit further, one can get a visual proof of (the 3-4-5 triangle instance of) Pythagoras' theorem:
  16. aeh5040
    Sounds like a potentially useful tool! It is worth considering non-right angle triangles, which can also be very useful for producing specified angles. For example, a 5-7-8 triangle has an exact 60 degree angle. Such angles can be computed using the Cosine Rule. I seem to remember I also wrote a python script to explore these a while back, and I may have posted some of the results here...
  17. aeh5040
    Yeah, I basically came to a similar conclusion. One could substitute old "rough" connectors or pin connectors (around an axle) for the smooth connectors, but it doesn't seem to help much...
  18. aeh5040
    Wow - you must have quite a collection of angle connectors!
  19. aeh5040
    Many thanks AlphaZed for this - the LDD file is almost exactly right. You have inspired me to make instructions! They can be downloaded here: http://rebrickable.com/mocs/aeh5040/slithy-toves-kinetic-sculpture You are correct that the geometry is not mathematically perfect. I had to do some faking to make it fit in the LDraw file...
  20. aeh5040
    Very cool! I knew you would find some unusual use for the new circular racks.
  21. aeh5040
    Amazing!
  22. aeh5040
    That's a really nice little model! The clamp mechanism is particularly interesting. It looks like a huge amount of work to make instructions this way. You might want to look into LDraw+LPub - I think that ends up more efficient after the initial learning curve.
  23. aeh5040
    Cool! Absolutely, please do post it.
  24. aeh5040
    Here you go: http://rebrickable.com/mocs/aeh5040/linked-cranks-puzzle
  25. aeh5040
    Wow! I think this could be one of my favorites of all time. I love the organic motion.
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