1. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    27 Oct '09 18:26
    Imagine you have a supply of perfectly uniform bricks of length 1, and you'd like to build a freestanding bridge of sorts. How far could this bridge theoretically extend if it is composed of bricks placed on top of once another in a single strip?

    For example, a bridge made of 3 bricks resting on the ground would look something like this from the side:

    . . . . ____
    . . . ____
    . . ____
    **************(ground)
  2. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    27 Oct '09 20:40
    it could go forever, given the proper placment.
  3. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    27 Oct '09 20:57
    Originally posted by joe shmo
    it could go forever, given the proper placment.
    Of course, the real question is can you prove it?
  4. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    27 Oct '09 22:07
    Originally posted by PBE6
    Of course, the real question is can you prove it?
    no, I cant prove it.
  5. Standard memberjoneschr
    Some guy
    Joined
    22 Jan '07
    Moves
    12299
    27 Oct '09 22:57
    Originally posted by PBE6
    Of course, the real question is can you prove it?
    Sure, just give me some bricks and some mortar.
  6. Standard memberuzless
    The So Fist
    Voice of Reason
    Joined
    28 Mar '06
    Moves
    9908
    28 Oct '09 02:51
    Originally posted by PBE6
    Imagine you have a supply of perfectly uniform bricks of length 1, and you'd like to build a freestanding bridge of sorts. How far could this bridge theoretically extend if it is composed of bricks placed on top of once another in a single strip?

    For example, a bridge made of 3 bricks resting on the ground would look something like this from the side:

    . . . . ____
    . . . ____
    . . ____
    **************(ground)
    reverse cantelever every other brick.


    lay one brick down
    place the next one 2/3 of an overhang.
    place the next one 1/3 hanging back the opposite way
    place the next one 2/3 of an overhang

    etc etc
  7. Standard memberuzless
    The So Fist
    Voice of Reason
    Joined
    28 Mar '06
    Moves
    9908
    28 Oct '09 02:521 edit
    an easier way would be to just build your bridge in the shape of an arch but i'm not sure if this is what you had in mind when you said one strip.
  8. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    28 Oct '09 15:33
    Originally posted by uzless
    reverse cantelever every other brick.


    lay one brick down
    place the next one 2/3 of an overhang.
    place the next one 1/3 hanging back the opposite way
    place the next one 2/3 of an overhang

    etc etc
    Nope, that only works for the first brick or the first 3 bricks. After that, it falls over.
  9. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    28 Oct '09 15:35
    Originally posted by uzless
    an easier way would be to just build your bridge in the shape of an arch but i'm not sure if this is what you had in mind when you said one strip.
    That's a good point, actually. I should have used the word "staircase" instead of "bridge".
  10. Standard memberjoneschr
    Some guy
    Joined
    22 Jan '07
    Moves
    12299
    28 Oct '09 17:14
    It can grow infinitely, but, you need to counterbalance each brick with enough weight, so that no one brick tips.

    So, every brick must have more weight on the overlapping part beneath it, than the part standing free (or else the obvious happens).

    So, you just need to make sure that you add additional weight to compensate for all the bricks that you add to the right.

    So, your "bridge" looks something like:
    |
    |
    | |
    | |
    | __
    |__
    __
    __

    It's a funny looking bridge, but it can get as long (and high at the same time) as you want it to.
  11. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    28 Oct '09 17:28
    Originally posted by joneschr
    It can grow infinitely, but, you need to counterbalance each brick with enough weight, so that no one brick tips.

    So, every brick must have more weight on the overlapping part beneath it, than the part standing free (or else the obvious happens).

    So, you just need to make sure that you add additional weight to compensate for all the bricks that you ad ...[text shortened]... a funny looking bridge, but it can get as long (and high at the same time) as you want it to.
    I think you're hovering around the right idea, but you don't need extra weight on the back end of the staircase to balance everything. The greatest length bridge can be achieved with one brick per level, no back-weighting.

    HINT: Each subset of bricks must balance on that subset's foundation brick...try starting with the smallest subset and see what happens!
  12. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
    Moves
    7733
    28 Oct '09 18:59
    Originally posted by PBE6
    I think you're hovering around the right idea, but you don't need extra weight on the back end of the staircase to balance everything. The greatest length bridge can be achieved with one brick per level, no back-weighting.

    HINT: Each subset of bricks must balance on that subset's foundation brick...try starting with the smallest subset and see what happens!
    It might have something to do with the fact that the series

    Sum(n=1,infinity)1/n is a divergent series.
  13. Standard memberPBE6
    Bananarama
    False berry
    Joined
    14 Feb '04
    Moves
    28719
    28 Oct '09 19:17
    Originally posted by joe shmo
    It might have something to do with the fact that the series

    Sum(n=1,infinity)1/n is a divergent series.
    It may indeed. 😉
  14. Subscribersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
    Moves
    52724
    14 Dec '09 13:59
    Originally posted by PBE6
    That's a good point, actually. I should have used the word "staircase" instead of "bridge".
    of course if that butterfly that changed the weather in Brazil were to land on top....
Back to Top