Penny bridge

What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?

Is that a theoretical or practical question?

Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

Since 1+1/2+1/3.... is infinity, then the length is infinite.

http://www.fincher.org/CoinStacking/HowTo.shtml

Originally posted by Dejection
Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

Since 1+1/2+1/3.... is infinity, then the length is infinite.

Well, ok, that is a theoretical result. I'd like to see someone try to successfully use that to bridge even 5 units of length (2.5 units from each side).

The website above shows a practical success of a three penny distance, using some counterbalance techniques. Counterbalance with your cards would probably make bridge building much easier.

1+1/2+1/3+1/4... never reaches 9.

Originally posted by doodinthemood
1+1/2+1/3+1/4... never reaches 9.

Yes, it does. The series 1/1+1/2+1/3+...1/n is asymptotic to ln(n); ln(n) reaches 9 for n=8103-and-a-bit.

Richard

Originally posted by doodinthemood
1+1/2+1/3+1/4... never reaches 9.

It does. The easy way to look at it is this:

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

> 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

= 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...

I got a different result. My series ended up being the inverse factorial series, not the harmonic series. Have to double check the calculations... 😕

Originally posted by mtthw
It does. The easy way to look at it is this:

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

> 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

= 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...

Is this like exponential decay?

Originally posted by PBE6
What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?

So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.😉

Originally posted by uzless
So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.😉

thats a minimum of 226 coins (I think)

7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

🙄

Originally posted by wolfgang59
thats a minimum of 226 coins (I think)

7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

🙄

Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins... 🙄

OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

This series is divergent, so the theoretical length of the bridge is infinite.

Originally posted by PBE6
Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins... 🙄

OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

This series is divergent, so the theoretical length of the bridge is infinite.

😲

5 COINS is not worth posting about!!! I assumed a 5 coin width!

Originally posted by wolfgang59
😲

5 COINS is not worth posting about!!! I assumed a 5 coin width!

Far be it for anyone to post a bit of humour. I got up to 10 before they crashed onto the carpet and rolled down the office hallway