It's definitely possible, friction or no friction.
I think your series of distances is off. Say the leading edge of the top penny is at 0, and the trailing edge is at 1. Then the second penny has to start at 1/2.
The center of mass of these two is at 3/4, so that's where the third penny starts. Similarly, the fourth penny starts at 11/12, and the fifth at 50/48.
So with only five pennies, carefully balanced, the top penny can extend completely past the base.
Well, what do you know. Of course! I think this problem does an excellent job of illustrating the dangers of generalizing a perceived pattern too soon. 0, 1/2, 3/4, NOT 7/8 as I had assumed! So now what I'm wondering is: Is there some finite limit to how far that last penny can go? Or with an infinite supply of pennies could you get the top penny as far displaced horizontally from the bottom one as you like? And is the natural "greedy" algorithm guaranteed to find the global optimum?
It's definitely possible, friction or no friction.
I think your series of distances is off. Say the leading edge of the top penny is at 0, and the trailing edge is at 1. Then the second penny has to start at 1/2.
The center of mass of these two is at 3/4, so that's where the third penny starts. Similarly, the fourth penny starts at 11/12, and the fifth at 50/48.
So with only five pennies, carefully balanced, the top penny can extend completely past the base.
Nice problem!
Prepoceros 3 years ago
Well, what do you know. Of course! I think this problem does an excellent job of illustrating the dangers of generalizing a perceived pattern too soon. 0, 1/2, 3/4, NOT 7/8 as I had assumed! So now what I'm wondering is: Is there some finite limit to how far that last penny can go? Or with an infinite supply of pennies could you get the top penny as far displaced horizontally from the bottom one as you like? And is the natural "greedy" algorithm guaranteed to find the global optimum?
TheMathGuy 3 years ago
YouTube is the ultimate time sink - good luck putting your life back together!
wogsland 3 years ago
Welcome back. I'm sorry too see you go.
DrZarkloff 3 years ago
This has been flagged as spam show
How can you do this to us!!! xD
LOLZ...
CleverDjembe 3 years ago
maybe your desk is slightly tilted
atypicalguy 3 years ago
That's cool man, take care of yourself.
I went ahead and subbed to your other channels too.
And the penny thing, I have no idea, I was hoping that you could teach me that :P
KashEzy 3 years ago
For some reason fractions kept coming up in my mind, but I'm sorta drunk so math is useless right about now.
Please make math vids when you find the time. :)
KashEzy 3 years ago
Have a nice break Nate.
CousinoMacul 3 years ago