- #1

Chewy0087

- 368

- 0

## Homework Statement

When dominos are stacked one on top of each other on the edge of the table, it turns out that the overhangs are related to the harmonic numbers Hn, which are defined as 1 + 1/2 + 1/3 + ... + 1/n: the maximum overhang (over the edge of the table) possible for n dominos is Hn/2.

Using the concept of centre of gravity prove this, feel free to use diagrams to aid your explanation.

## The Attempt at a Solution

I'm struggling with this one, and even having looked it up it's not at all clear to me, from what i thought, the centre of mass of all of the books together must be on the pivot point (at least), over the edge of the table, with 1/2 of the first domino over the side, however I really can't justify to myself that placing another domino ontop will keep it balanced, I read somewhere that " The center of gravity of the stack of two books is at the midpoint of the books' overlap" what exactly does this mean? I've tried drawing diagrams, don't understand it.

Thanks in advance for any help & i'll try and scan in a picture although I don't think my diagram will help

Edit: Hmm looking over it again I get the feeling that for any pile the centre of gravity of the ENTIRE pile must be on the pivot point, however how would you go about working this out mathematically for say 10 books?

Last edited: