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Domino Overhangs – Fall 2013

November 3, 2013

Saturday, November 2, 2013

Our question was: How big of an overhang is possible when stacking dominoes?

We built with dominoes to gather intuition.  We found two strategies that we called “Stairs” (the more of a cantilever approach) and “Toy Sword” (counterweights placed on the middle — if  you outline it with creativity, you can see a toy sword.)

We have not yet stated any rules so both options are valid.  At some point no one had complained about my dominoes (which are very imperfect) so I asked them to think about what a perfect domino is while they were building.

One of them said loudly, “Sticky!’  Which would, of course, be great!

We have overhangs of 0.80 with Stairs and almost 2 with Toy Swords.  With 20 minutes to go we put the dominoes away so we could focus on what we we noticed.

We have two conjectures.  The first conjecture is that with really good dominoes we can get an overhang of two dominoes (note that “overhang” is still undefined but they are all using the same intuitive definition) with Toy Sword.  The second conjecture is that we could get infinitely close to an overhang of one domino with Stairs.

They gave a beautiful explanation of how, using one perfect (“perfect” only partially defined) domino as a base, one can get an overhang of infinitely close to 1/2 with a second domino (first non-base domino).

Measuring a “Stair”:

Stair

Measuring a “Toy Sword”:

TS

 

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