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)
Originally posted by PBE6reverse cantelever every other brick.
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)
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
Originally posted by uzlessNope, that only works for the first brick or the first 3 bricks. After that, it falls over.
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
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.
Originally posted by joneschrI 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.
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.
HINT: Each subset of bricks must balance on that subset's foundation brick...try starting with the smallest subset and see what happens!
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Originally posted by PBE6It might have something to do with the fact that the series
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!
Sum(n=1,infinity)1/n is a divergent series.